The chapter “Motion in One Dimension” introduces the fundamental concepts of describing the movement of an object along a straight line. It begins by defining key terms like distance (the total path length covered, a scalar quantity) and displacement (the shortest straight-line distance between the start and end points, a vector quantity). Similarly, it distinguishes between speed (the rate of covering distance, a scalar) and velocity (the rate of change of displacement, a vector). The concept of acceleration is introduced as the rate of change of velocity, which can be positive (speeding up) or negative (slowing down, also called retardation). A body is said to be in uniform motion when it covers equal distances in equal intervals of time, meaning its speed is constant.
A major focus of the chapter is on the graphical representation of motion and the derivation of essential equations. By studying distance-time graphs, one can determine the speed of an object, where the slope of the graph gives the speed (or velocity). More importantly, velocity-time graphs are explored in detail. The slope of a velocity-time graph gives the acceleration of the object, while the area under the graph represents the displacement covered. These graphical insights lead to the derivation of the three fundamental equations of motion for uniformly accelerated motion: v=u+at, s=u+1/2at, and u2+2as, where uu is initial velocity, vv is final velocity, aa is acceleration, tt is time, and ss is displacement.
Finally, the chapter applies these concepts to a specific and important case: motion under gravity. The acceleration due to gravity (g), which is approximately 9.8 m/s2 directed towards the centre of the Earth, is used as a constant acceleration in the equations of motion. This allows for the analysis of objects in free fall or those projected vertically upwards. Students learn to solve numerical problems by substituting aa with +g or −g depending on the direction chosen as positive, thereby calculating quantities like maximum height reached, time of flight, and velocity upon hitting the ground for objects moving vertically.
Exercise 2 (A)
Question 1.
Differentiate between the scalar and vector quantities, giving two examples of each.
Ans:
| Feature | Scalar Quantity | Vector Quantity |
| Definition | A physical quantity fully described by its magnitude (size or numerical value) alone. | A physical quantity fully described by both magnitude and direction. |
| Direction | Has no associated direction. | Has a specific direction in space. |
| Addition | Follows ordinary rules of algebra (simple arithmetic). | Follows special rules of vector algebra (e.g., triangle law, parallelogram law). |
| Examples | Mass, Time, Speed, Temperature, Distance, Energy. | Force, Velocity, Acceleration, Displacement, Momentum. |
Examples
Scalar Quantities
- Mass: A person’s mass is 70 kg, regardless of direction.
- Time: The duration of a trip is 2 hours, which is a value only.
Vector Quantities
- Velocity: A car is moving at 60 km/h East. (Magnitude and direction).
- Force: A push of 10 Newtons applied downward on a box. (Magnitude and direction).
Question 2.
State whether the following quantity is a scalar or vector.
- Pressure
- Force
- Momentum
- Energy
- Weight
- Speed
Ans:
| Quantity | Classification | Reason |
| Pressure | Scalar | It has magnitude but no unique direction; it acts in all directions on a surface. |
| Force | Vector | It has both magnitude (strength) and a specific direction (the way the push or pull is applied). |
| Momentum | Vector | It is the product of mass (scalar) and velocity (vector), so it has the same direction as velocity. |
| Energy | Scalar | It is a measure of the capacity to do work and is not associated with a specific direction. |
| Weight | Vector | It is a measure of the gravitational force on an object, acting specifically downward toward the center of the celestial body. |
| Speed | Scalar | It is the rate of motion (distance over time) and is defined only by its magnitude. |
Question 3.
When is a body said to be at rest?
Ans:
A body is said to be at rest if its position does not change with respect to its surroundings (or a defined reference point) over a period of time.
In physics, the state of rest is relative, meaning it depends entirely on the observer’s frame of reference.
- Simple View: A book lying on a table is at rest with respect to the table and the room.
- Physics View (Relativity): That same book is in motion with respect to the Sun because the Earth is constantly moving (rotating and orbiting). Therefore, an object is only “at rest” relative to what you choose to compare it with.
Question 4.
When is a body said to be in motion?
Ans:
An object is defined as being in motion when its location shifts relative to a chosen point of reference as time elapses.
Question 5.
What do you mean by motion in one direction?
Ans:
Motion in one direction, also known as one-dimensional motion or rectilinear motion, is the movement of an object exclusively along a single straight line without any change in the path’s direction.
Essentially, it is the simplest form of motion in physics:
- Straight Path: The object’s entire trajectory is a straight line.
- Single Axis: The movement can be fully described using only one spatial coordinate (like the x-axis for horizontal motion or the y-axis for vertical motion).
- Unchanging Direction: The object does not turn, swerve, or veer off the straight path. It moves either forward or backward along that single line.
Question 6.
Define displacement. State its unit.
Ans:
Displacement: A Unique Definition
Displacement (Δx) is defined as the change in position of an object. It is the straight-line distance measured from an object’s starting point to its ending point, which necessarily includes the direction of that change.
It is a vector quantity, characterized by both its size (magnitude) and its orientation.
The mathematical formula for calculating displacement is:
Δx=xf−xi
Where:
- Δx is the displacement.
- xf is the final position.
- xi is the initial position.
The standard unit of displacement within the International System of Units (SI) is the meter (m).
Question 7.
Differentiate between distance and displacement.
Ans:
| Feature | Distance | Displacement |
| Definition | The total length of the actual path covered by an object during its motion. | The shortest straight-line path between the object’s initial and final positions. |
| Type of Quantity | Scalar quantity (only magnitude). | Vector quantity (both magnitude and direction). |
| Value | Can only be positive (or zero if the object is stationary). | Can be positive, negative, or zero. |
| Path Dependence | Depends on the actual path taken. | Independent of the path taken; only depends on the start and end points. |
| Relationship | Always greater than or equal to the magnitude of the displacement ($\text{Distance} \ge | \text{Displacement} |
Question 8.
Can displacement be zero even if the distance is not zero? Give one example to explain your answer.
Ans:
The concept that displacement can be zero even if the distance is not zero arises from the definitions of these two quantities:
- Displacement (Δx) is a vector quantity that measures the shortest straight-line change in an object’s position, calculated as:
Δx=xfinal−xinitial - Distance is a scalar quantity that measures the total length of the path actually traveled by the object.
Explanation of the Phenomenon
When an object in motion returns to its exact starting point, its displacement is zero, even though it has covered a non-zero distance.
- Zero Displacement: If the object’s final position (xfinal) is identical to its initial position (xinitial), the net change in position is zero.
Δx=xinitial−xinitial=0 - Non-Zero Distance: Distance, however, measures every segment of the path taken. As long as the object moved at all, the total path length (distance) will be a positive, non-zero value.
Illustrative Example
Consider a cyclist who completes a closed loop or circuit.
| Quantity | Value | Reasoning |
| Distance | 5 kilometers (non-zero) | This is the total length of the road or path the cyclist traveled. |
| Displacement | 0 kilometers (zero) | The cyclist’s journey ended precisely where it began, resulting in no net change in position. |
Question 9.
When is the magnitude of displacement equal to the distance?
Ans:
The magnitude of displacement is equal to the distance traveled when a body moves along a straight line in a single, fixed direction without changing its path or reversing its course.
- Distance is the total length of the path covered (a scalar quantity).
- Displacement is the shortest straight-line distance between the starting and ending points (a vector quantity).
When motion is strictly along a straight line and does not turn back, the total path length is the same as the shortest distance between the start and end points.
Question 10.
Define velocity. State its unit.
Ans:
Velocity is formally defined as the rate at which an object changes its position in a specific direction. It is a vector quantity, which fundamentally means its description includes two essential components:
- Magnitude (Speed): This describes how fast the object is moving.
- Direction: This specifies the orientation or path of the movement.
Formula and Unit
The mathematical expression for average velocity (v) is the ratio of the change in displacement (Δd) to the corresponding change in time (Δt):
v=Δt / Δd
The SI unit (International System of Units) for velocity is metres per second (m/s) or m⋅s−1.
Question 11.
Define speed. What is its S.I. unit?
Ans:
Speed is defined as the rate at which an object covers distance.
It is a scalar quantity that only indicates how fast an object is moving, without regard to the direction of motion.
Mathematically, it is calculated as:
Speed=Time Taken / Distance Traveled
The S.I. (International System) unit of speed is:Metre per second (m/s or m⋅s−1)
Question 12.
Distinguish between speed and velocity.
Ans:
| Feature | Speed | Velocity |
| Definition | The rate at which an object covers distance. | The rate at which an object changes its displacement (position). |
| Quantity Type | Scalar | Vector |
| Components | Has magnitude (size) only. | Has magnitude (speed) and direction. |
| Formula | Average Speed =Total Time / Total Distance | Average Velocity =Total Time / Displacement |
| Possible Values | Always positive or zero (never negative). | Can be positive, negative, or zero. |
| Direction Change | An object can change direction without its speed changing (e.g., driving in a circle at 60 km/h). | A change in direction always results in a change in velocity, even if the speed is constant. |
| Example | 50 km/h | 50 km/h East |
Question 13.
Which quantity-speed or velocity-gives the direction of motion of a body?
Ans:
The concept that defines a body’s direction of movement is velocity.
Velocity is classified as a vector quantity, which means its description requires both a magnitude (how fast the body is moving, or its speed) and a direction (the way it is traveling). Conversely, speed is a scalar quantity; it only indicates the rate of motion without any reference to the path or direction taken.
Question 14.
When is instantaneous speed the same as the average speed?
Ans:
The instantaneous speed of a body is equal to its average speed only when the body’s motion is characterized by uniform (constant) speed throughout the entire time interval.
Here’s a concise explanation of why this is the case:
- Uniform Speed: This state means the object covers equal distances in equal intervals of time. The value of the speed never changes.
- Instantaneous Speed: This is the speed of the object measured at one specific, precise moment. If the speed is uniform, this measurement is the same constant value at every instant.
- Average Speed: This is the total distance traveled divided by the total time taken.
When the speed remains constant throughout the journey, the value of the speed at any single instant (instantaneous speed) is the same as every other instant. Therefore, calculating the average of all these identical values over the total time must also yield that same constant value (average speed = instantaneous speed).
Question 15.
Distinguish between uniform velocity and variable velocity.
Ans:
The distinction between uniform and variable velocity lies in whether the body’s rate of displacement remains constant or changes over time.
Uniform Velocity
An object is said to have uniform velocity (or constant velocity) if it travels with equal displacements in equal intervals of time, regardless of how small those intervals are.
| Characteristic | Description |
| Definition | The magnitude (speed) and direction of the body’s velocity remain constant over time. |
| Path of Motion | Must be a straight line (rectilinear motion). |
| Acceleration | Zero (a=0), because the velocity is not changing. |
| Example | A train moving at a steady 60 km/h East along a straight, level track. |
Variable Velocity (Non-Uniform Velocity)
An object is said to have variable velocity if its velocity changes over a period of time. Since velocity is a vector quantity, a change in either its magnitude or its direction will result in variable velocity.
| Characteristic | Description |
| Definition | The velocity changes over time, meaning either the magnitude (speed), the direction, or both are changing. |
| Path of Motion | Can be a straight line (if speed changes) or a curved path (if direction changes). |
| Acceleration | Non-zero (a=0), as a change in velocity defines acceleration. |
| Example | A car slowing down at a traffic light (speed changes) or an object moving in a circle at a constant speed (direction changes). |
Question 16.
Distinguish between average speed and average velocity.
Ans:
| Feature | Average Speed | Average Velocity |
| Definition | Ratio of total distance traveled to the total time taken. | Ratio of total displacement (change in position) to the total time taken. |
| Formula | Average Speed=Total Time / Total Distance | Average Velocity=Total Time / Total Displacement |
| Type of Quantity | Scalar (magnitude only, no direction). | Vector (both magnitude and direction). |
| Value in Round Trip | Cannot be zero (if motion occurred, distance is positive). | Can be zero (if the object returns to its starting point, displacement is zero). |
| Path Dependence | Depends on the actual path taken (distance). | Depends only on the initial and final positions (displacement). |
Question 17.
Give an example of the motion of a body moving with a constant speed but with a variable velocity. Draw a diagram to represent such a motion.
Ans:
Example: Uniform Circular Motion
- Constant Speed (Scalar): The object covers the same distance in every unit of time. The magnitude of its velocity (the speed) remains unchanged. For instance, a car driving around a perfectly circular track always at 40 km/h.
- Variable Velocity (Vector): Although the speed is constant, the direction of the motion is continuously changing as the object follows the curve of the circle. Since velocity is a vector quantity (magnitude + direction), a change in direction means the velocity itself is changing.
This change in velocity results in an acceleration that is always directed toward the center of the circle (called centripetal acceleration).
Diagram Representation
The motion can be represented by a circle with velocity vectors drawn tangentially at different points.
In the diagram:
- Magnitude (Speed): The length of the velocity vectors (v1, v2, v3) is the same, indicating constant speed.
- Direction (Velocity): The direction of the velocity vectors is different at every point (tangent to the circle), indicating a variable velocity.
- Acceleration (a): The acceleration vector always points toward the center of the circle, showing the direction of the change in velocity.
Question 18.
Give an example of motion in which the average speed is not zero but the average velocity is zero.
Ans:
This condition occurs when a body returns to its starting point after having moved for some time.
- Average Velocity is Zero:
Average Velocity=Total Time / Total Displacement
Since the body ends up at the same place it started, the Total Displacement (the shortest distance between the initial and final position) is zero, making the average velocity zero. - Average Speed is Non-Zero:
Average Speed=Total Time / Total Distance Traveled
The body actually traveled a path, so the Total Distance Traveled is non-zero, resulting in a non-zero average speed.
Example
A car drives one lap around a circular race track.
Question 19.
Define acceleration. State its unit.
Ans:
Acceleration describes how an object’s velocity transforms over a specific time interval. Since velocity combines speed with direction, acceleration occurs whenever there is a change in the object’s speed, its direction of travel, or both. Essentially, it quantifies how swiftly motion is being altered.The mathematical expression for average acceleration is the difference between the final and initial velocity divided by the time taken for that change, or a = (v – u)/t.As a derived vector quantity, its standard unit in the International System (SI) is the meter per second squared (m/s²). This unit logically follows from its definition: it represents the change in velocity (measured in m/s) that occurs during each second of time.
Question 20.
Distinguish between acceleration and retardation.
Ans:
| Aspect | Acceleration | Retardation (Deceleration) |
| Basic Meaning | The rate at which the velocity increases with time. | The rate at which the velocity decreases with time. |
| Mathematical Sign | Generally considered positive (+a). | Defined as negative acceleration (−a). |
| Direction of Force/Vector | The acceleration vector acts in the same direction as the motion/velocity. | The acceleration vector acts opposite to the direction of the motion/velocity. |
| Effect on Speed | Causes the object’s speed to increase. | Causes the object’s speed to decrease. |
| Example | A car pressing the gas pedal to pass another vehicle. | A car applying the brakes to stop at a red light. |
Question 21.
Differentiate between uniform acceleration and variable acceleration.
Ans:
Uniform Acceleration (Constant Acceleration)
Definition: A body is said to be in uniform acceleration when its velocity changes by equal amounts in equal intervals of time, regardless of how small those time intervals are. This means the acceleration remains constant in both magnitude and direction.
| Characteristic | Description |
| Acceleration Value | Constant (e.g., 5 m/s2 at t=1 s, t=2 s, and t=3 s). |
| Velocity Change | Equal change in velocity (Δv) for every equal time interval (Δt). |
| Motion Type | Possible to use the standard equations of motion (kinematic equations). |
| Example | An object in free fall (ignoring air resistance), where the acceleration is constant, a=9.8 m/s2 (or g). |
| v−t Graph | A straight line with a non-zero, constant slope. |
Variable Acceleration (Non-Uniform Acceleration)
Definition: A body is said to be in variable acceleration when its velocity changes by unequal amounts in equal intervals of time. This means the acceleration is not constant; it changes in magnitude, direction, or both over time.
| Characteristic | Description |
| Acceleration Value | Changes with time (e.g., a might be 3 m/s2 at t=1 s and 7 m/s2 at t=2 s). |
| Velocity Change | Unequal change in velocity (Δv) for equal time intervals (Δt). |
| Motion Type | Requires calculus (differentiation and integration) to accurately describe the motion. |
| Example | A car driving in heavy traffic, constantly speeding up, slowing down, and turning. |
| v−t Graph | A curved line with a slope that continuously changes. |
Question 22.
What is meant by the term retardation? Name its S.I. unit.
Ans:
The term retardation is an older or alternative term used in physics to mean negative acceleration or deceleration.
Retardation
Retardation is defined as the rate of decrease of velocity of a body with respect to time.
It occurs when the acceleration vector of a moving object is directed opposite to its velocity vector, causing the object to slow down.
- Example: When a driver applies the brakes on a car, the car is undergoing retardation.
S.I. Unit
Since retardation is a form of acceleration, its S.I. unit is the same as that of acceleration.
S.I. unit of Retardation=metre per second squared(m/s2)
Question 23.
Which of the quantity-velocity or acceleration-determines the direction of motion?
Ans:
The direction of motion of a body is determined by its velocity.
Here’s a brief explanation:
- Velocity (v): This vector quantity describes both the speed and the current direction of the body. The direction of the velocity vector is always the direction in which the object is moving at that instant.
- Acceleration (a): This vector quantity describes the rate of change of velocity. It indicates how the velocity is changing (getting faster, slower, or turning), but not necessarily the direction the body is currently moving.
Example: Imagine you throw a ball straight up.
- Going Up: The velocity is directed upward (direction of motion). The acceleration (due to gravity) is directed downward.
- At the Peak: The instantaneous velocity is zero (the body stops moving for a moment). The acceleration is still directed downward.
- Coming Down: The velocity is directed downward (direction of motion). The acceleration is also directed downward.
Question 24.
(a) Give one example of following motion : Uniform velocity
(b) Give one example of following motion : Variable velocity
(c) Give one example of following motion : Variable acceleration
(d) Give one example of the following motion: Uniform retardation
Ans:
| Motion Type | Example |
| (a) Uniform Velocity | A train moving along a straight, level track at a constant speed, such as 80 km/h without changing its direction. |
| (b) Variable Velocity | A car driving around a circular racetrack at a constant speed of 100 km/h. The car’s speed is constant, but its direction (and thus its velocity) is continuously changing. |
| (c) Variable Acceleration | A rocket launching into space where its engine thrust (force) and the amount of fuel remaining (mass) constantly change. Since acceleration (a) is defined by Force/Mass, both the magnitude and direction of its acceleration vary significantly over time. |
| (d) Uniform Retardation | A skater gliding across a horizontal, rough ice rink who initially pushes off and then glides to a stop. The force of friction is nearly constant and acts opposite to the direction of motion, causing a uniform decrease in velocity (constant negative acceleration). |
Question 25.
The diagram below shows the pattern of the oil on the road at a constant rate from a moving car. What information do you get from it about the motion of the car?
Ans:
The information you get about the motion of the car depends entirely on the spacing of the oil drops.
Since the oil is dripping at a constant rate, the time interval between any two consecutive drops is always the same (e.g., one drop every second). Therefore, the distance between the drops directly indicates the speed of the car during that time interval.
Based on the general interpretation of oil drop patterns:
- If the drops are equally spaced (Constant distance between drops):
- The car is covering equal distances in equal intervals of time.
- This indicates the car is moving with Uniform Velocity (constant speed).
- If the distance between the drops is increasing:
- The car is covering increasing distances in equal intervals of time.
- This indicates the car is accelerating (speeding up).
- If the distance between the drops is decreasing:
- The car is covering decreasing distances in equal intervals of time.
- This indicates the car is decelerating (slowing down).
In the specific image provided in the context (which is not visible to me but is a common exam question):
- The usual pattern shown in this context is a combination: Equally spaced drops followed by drops that are closer together.
If the pattern shows initial uniform spacing followed by decreasing spacing, the information is:
- The car initially moved with a constant speed (uniform velocity) and then slowed down (deceleration/non-uniform motion).
Question 26.
Define the term acceleration due to gravity. State its average value.
Ans:
Acceleration Due to Gravity (g)
Acceleration due to gravity is the constant acceleration experienced by a body in free fall (i.e., moving solely under the influence of gravity) towards the center of a massive object, such as a planet.
It is denoted by the letter g and represents the rate at which the velocity of a freely falling object increases every second. Crucially, it is independent of the mass of the falling object (ignoring air resistance).
Average Value
The standard, or average, value of acceleration due to gravity on the surface of the Earth is approximately:
g≈9.8 m/s2
This is often used for calculations near the Earth’s surface. The precise value varies slightly with factors like altitude, latitude (being slightly greater at the poles than at the equator), and local geology.
Question 27.
‘The value of g remains the same at all places on the Earth’s surface’. Is this statement true? Give reason for your answer.
Ans:
Reason for Variation in g
The acceleration due to gravity (g) varies slightly across the Earth’s surface due to two main factors: the shape of the Earth and its rotation.
1. Earth’s Shape (Latitude)
The formula for acceleration due to gravity is g=R2GM, where R is the radius from the center of the Earth.
- The Earth is not a perfect sphere; it is an oblate spheroid, meaning it’s slightly flattened at the poles and bulges at the equator.
- The equatorial radius (Re) is greater than the polar radius (Rp).
- Since g is inversely proportional to R2, a larger radius results in a smaller value of g.
- Therefore, g is minimum at the Equator (largest radius).
- g is maximum at the Poles (smallest radius).
2. Earth’s Rotation
- The rotation of the Earth creates an outward centrifugal force that partially counteracts the gravitational pull.
- This centrifugal effect is maximum at the Equator (where the rotational speed is highest) and zero at the Poles.
- This outward force reduces the effective value of g most significantly at the equator, contributing to its minimum value there.
For these reasons, the value of g ranges from approximately 9.78 m/s2 at the equator to 9.83 m/s2 at the poles. The conventional average value used in calculations is 9.8 m/s2.
Question 28.
If a stone and a pencil are dropped simultaneously in vacuum from the top of a tower, then which of the two will reach the ground first? Give a reason.
Ans:
Reason
The reason is that in a vacuum, the only force acting on both objects is gravity.
- Acceleration is Independent of Mass: Near the Earth’s surface, the acceleration due to gravity (g) is constant for all objects, approximately 9.8 m/s2. This acceleration is independent of an object’s mass.
- No Air Resistance: The term “in a vacuum” means there is absolutely no air resistance or drag force to oppose the motion.
- Conclusion: Since both the heavy stone and the light pencil start from rest, fall through the same distance, and experience the exact same downward acceleration (g), their velocities and the time taken to reach the ground must be equal.
Exercise 2 (A)
Question 1.
The vector quantity is :
- Work
- Pressure
- Distance
- Velocity
Ans: Velocity is a Vector quantity. The others are all Scalar quantities.
Question 2.
The S.I. unit of velocity is ___________
- km h-1
- m min-1
- km rnin-1
- m s-1
Question 3.
The unit of retardation is ____________
- m s-1
- m s-2
- m
- m s2
Question 4.
A body when projected up with an initial velocity u goes to a maximum height h in time t and then comes back at the point of projection. The correct statement is ______________
- The average velocity is 2 h/t.
- The acceleration is zero.
- The final velocity on reaching the point of projection is 2 u.
- The displacement is zero.
Question 5.
18 km h-1 is equal to _____________
- 10 m s-1
- 5 m s-1
- 18 m s-1
- 1.8 m s-1
Exercise 2 (A)
Question 1.
The speed of a car is 72 km h-1. Express it in m s-1.
Ans:
Question 2.
Express 15 m s-1 in km h-1.
Ans:
Question 3.
(a) Express the following in m s−1. 1 km h−1
(b) Express the following in m s-1. 18 km min-1
Ans:
Question 4.
Arrange the following speeds in increasing order. 10 m s-1, 1 km min-1 and 18 km h-1.
Ans:
18 km h−1<10 m s−1<1 km min−1
Question 5.
A train takes 3 h to travel from Agra to Delhi with a uniform speed of 65 km h-1. Find the distance between the two cities.
Ans:
Calculation
This is a straightforward application of the distance, speed, and time relationship.
The formula relating distance (D), speed (S), and time (T) is:
Distance = Speed × Time
Given:
- Speed (S) = 65 km h−1
- Time (T) = 3 h
Substituting the values into the formula:
D=65 km h−1×3 h
D=195 km
Question 6.
A car travels the first 30 km with a uniform speed of 60 km h−1 and the next 30 km with a uniform speed of 40 km h−1. Calculate :
The total time of journey,
The average speed of the car.
Ans:
Question 7.
A train takes 2 h to reach station B from station A, and then 3 h to return from station B to station A. The distance between the two stations is 200 km. Find:
The average speed,
The average velocity of the train.
Ans:
Question 8.
( a) A car moving on a straight path covers a distance of 1 km due east in 100 s. What is the speed of the car?
(d) A car moving on a straight path covers a distance of 1 km due east in 100 s. What is the velocity of the car?
Ans:
Question 9.
A body starts from rest and acquires a velocity 10 m s-1 in 2 s. Find the acceleration.
10. A car starting from rest acquires a velocity 180m s-1 in 0.05 h. Find the acceleration.
Ans:
Final Answers:
- 5 m/s2
- 1 m/s2
Question 11.
A body is moving vertically upwards. Its velocity changes at a constant rate from 50 m s−1 to 20 m s−1 in 3 s. What is its acceleration?
Ans:
Analysis of the Calculation
The problem asks for the acceleration (a) of a body whose velocity changes from an initial value (u) to a final value (v) over a time interval (t).
The formula used is the definition of acceleration:
A = Time Taken / Change in Velocity =t / v−u
Step-by-Step Breakdown
- Identify Variables (with upwards as positive):
- Initial Velocity (u): +50 m/s
- Final Velocity (v): +20 m/s
- Time (t): 3 s
- Calculate Acceleration:
a=3 s / (20 m/s)−(50 m/s)
a=3 s / −30 m/s
a=−10.0 m/s2
Conclusion
The body’s acceleration is −10.0 m/s2.
This result means:
- The body is decelerating (slowing down) at a rate of 10.0 m/s every second.
- The acceleration vector points downwards (↓), which is physically expected for a body moving vertically near the Earth’s surface under the influence of gravity (g≈9.8 to 10 m/s2).
Question 12.
A toy car initially moving with uniform velocity of 18 km h-1 comes to a stop in 2 s. Find the retardation of the car in S.I. units.
Ans:
Retardation=∣a∣=∣−2.5 m/s2∣=2.5 m/s2
Question 13.
A car accelerates at a rate of 5 m s-2. Find the increase in its velocity in 2 s.
Ans:
Calculation
The increase in velocity (Δv) is the change in velocity, which is related to acceleration (a) and time (t) by the definition of acceleration:
a=tΔv
Therefore, the increase in velocity is:
Δv=a×t
Given Values:
- Acceleration (a) = 5 m/s2
- Time (t) = 2 s
Substitute the values:
Δv=5 m/s2×2 s
Δv=10 m/s
The velocity will increase by 10 m/s.
Question 14.
A car is moving with a velocity 20 m s-1. The brakes are applied to retard it at a rate of 2 m s-2. What will be the velocity after 5 s of applying the brakes?
Ans:
Calculation
This problem involves uniformly accelerated (or retarded) motion, which can be solved using the first equation of motion:
v=u+at
Given values:
- Initial velocity (u): 20 m/s
- Time (t): 5 s
- Retardation (deceleration, a): 2 m/s2
Since the car is retarding (slowing down), the acceleration must be taken as negative in the equation: a=−2 m/s2.
Substitute the values into the equation:
vvv=20 m/s+(−2 m/s2)×5 s=20 m/s−10 m/s=10 m/s
The final velocity (v) of the car after 5 s is 10 m/s.
Question 15.
A bicycle initially moving with a velocity 5.0 m s-1 accelerates for 5 s at a rate of 2 m s-2. What will be its final velocity?
Ans:
Calculation of Final Velocity
This is a problem of uniformly accelerated motion, which can be solved using the first equation of motion:
v=u+at
Given Values:
- Initial velocity (u) = 5.0 m/s
- Acceleration (a) = 2 m/s2
- Time (t) = 5 s
- Final velocity (v) = ?
Substitute the values:
v=5.0 m/s+(2 m/s2×5 s)
v=5.0 m/s+10 m/s
v=15.0 m/s
The final velocity of the bicycle is 15.0 m/s.
16. A car is moving in a straight line with speed 18 km h-1. It is stopped in 5 s by applying the brakes. Find:
the speed of car in m s-1
the retardation and
the speed of the car after 2 s of applying the brakes.
Ans:
