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Motion is a constant force in the universe. When there is a displacement in an object from its original position the motion is said to be done. Motion in a straight line refers to displacement of the object in a straight line. For example, motion of a lift is linear motion. It only moves up and down. Also, there are 2 types of linear motion; uniform linear motion and non-uniform linear motion. In a uniform motion the object moves with zero acceleration and constant velocity whereas in non-uniform motion the velocity varies and acceleration non-zero.
Ques 1. Which of the following are obtained by dividing total displacement by total time taken?
- Average velocity
- Instantaneous velocity
- Uniform velocity
- Speed
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Ans. (a) Average velocity
Explanation: The average velocity is obtained by dividing total displacement by total time taken. Instantaneous velocity is calculated at an instant and not over a period of time. Speed is distance divided by time. Velocity is said to be uniform when velocity at every instant is equal to the average velocity.
Ques 2. When a body is in the state of complete rest, what kind of energy does it possess?
- Potential energy
- Kinetic energy
- Total energy
- Heat energy
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Ans. (a) Potential energy
Explanation: When the body is in the state of rest, there is no motion. Hence there is no kinetic energy, hence the total energy of the body is stored as its potential energy. The total energy is the sum of kinetic and potential energies.
Ques 3. A car, initially at rest, travels 20 m in 4 sec along a straight line with constant acceleration. Find the acceleration of the car.
- 4.9 m/s2
- 2.5 m/s2
- 0.4 m/s2
- 1.6 m/s2
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Ans. (b) 2.5 m/s2
Explanation: Given: Initial velocity (u) = 0
Distance (s) = 20m
Time (t) = 4 sec
Now, S = ut + ½ at2
\ 20 = (0 x 20) + ½ x a x 42
20 = 0 + ½ x a x 42
Therefore, Acceleration (a) = 20/8 = 2.5 m/s2
Ques 4. A ball is dropped from a height of 80m. The distance travelled by it in the fourth second will be ___.
(g = 10 m/s2)
- 50 m
- 15 m
- 80 m
- 35 m
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Ans. (d) 35 m
Explanation: Distance travelled by a body in nth second is;
Sn = u + a/2 (2n – 1)
Given: The ball is dropped from 80 m height, so initial velocity (u) = 0 m/s
Acceleration due to gravity (a) = 10 m/s2
n = 4
For nth second,
Sn = u + a/2 (2n – 1)
Therefore,
Distance travelled in 4th second (S4) = 0 + 10/2 (2 x 4 – 1)
= 35 m
Ques 5. The slope of the velocity – time graph for retarded motion is
- Zero
- Positive
- Negative
- Neutral
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Ans. (c) Negative
Explanation: The slope of any graph is the ratio of the vertical change between two points to the horizontal change between the same points.
In velocity-time graph the velocity (v) is on the vertical axis and time (t) on the horizontal axis.
Hence, the slope is given by Slope = Dv/Dt
The rate of change of velocity is called acceleration; the slope of a velocity-time graph gives the acceleration.
The slope of the velocity-time graph for retarded motion is negative.
Ques 6. A body starts from rest and travels with a uniform acceleration of 20 m/s2. Calculate the time taken by the body to cover the distance of 90 m.
- 6s
- 3s
- 13s
- 12s
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Ans. (b) 3 s
Explanation: Given: acceleration (a) = 20m/s2
Distance travelled (s) = 90 m
Initial velocity (u) = 0
Time taken to cover 90 m is t
Now, S = ut + ½ at2
90 = 0 x t + ½ x 20 x t2
t2 = 9
Time taken (t) is 3 sec.
Read more about: Uniform Acceleration
Ques 7. The trajectory of an object is defined as x = (t-4)2, what is the velocity at t = 5?
- 2
- 5
- 1
- 4
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Ans. (a) 2
Explanation: The function for velocity can be derived by differentiating the equation with respect to t.
v = 2 (t - 4) is the required function.
When t = 5, v = 2 (5 - 4)
v = 2
Ques 8. A car is moving in a spiral starting from the origin with uniform angular velocity. What can be said about the instantaneous velocity?
- It increases with time
- It decreases with time
- It remains constant
- It does not depend on time
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Ans. (a) it increases with time
Explanation: This type of motion can be called circular motion with increasing radius. As the radius increases, the tangential velocity increases (v = rw). Now, as there is only one velocity present, the speed will be equal to the magnitude of the tangential velocity.
Read more: Angular Velocity
Ques 9. If two bodies are moving in opposite directions with non-zero velocities, which of the following statements is true?
- Relative velocity > Absolute velocity
- Relative velocity < Absolute velocity
- Relative velocity = Absolute velocity
- Relative velocity <= Absolute velocity
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Ans. (a) Relative velocity > Absolute velocity
Explanation: The formula for relative velocity is, Vector VR = Vector VA – Vector VB. When both the velocities are opposite in direction, the equation becomes VR = VA – (-VB). Hence the magnitudes add up making the relative velocity greater than the absolute velocity of any of the two bodies.
Ques 10. What does relative motion signify?
- The motion of a body with respect to other body
- Uniformly accelerated
- Non-uniformly accelerated
- Motion along a curve
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Ans. (b) Uniformly accelerated
Explanation: The three equations of motion are valid for uniformly accelerated motion. The equations do not work in situations where the acceleration is non-uniform. In that case it is better to work with the differential forms of velocity and acceleration.
Ques 11. What is the rate of change of rate of change of displacement of a body?
- Velocity
- Acceleration
- Force
- Jerk
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Ans. (b) Acceleration
Explanation: The rate of change of displacement of a body is velocity. The rate of change of rate of displacement of a body, or rate of change of velocity is acceleration.
Ques 12. Displacement between two points is ___
- The shortest path
- The longest path
- Equal to distance
- Greater than distance
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Ans. (a) the shortest path
Explanation: Displacement between two points is the shortest path between them. It is always less than or equal to the distance between them. Displacement can never be greater than distance.
Ques 13. What will the velocity v/s time graph of a ball falling from a height before hitting the ground look like?
- A straight line with positive slope
- A straight line with negative slope
- A straight line with zero slope
- A parabola
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Ans. (a) a straight line with positive slope
Explanation: As the ball falls down, its velocity increases. This is because of the acceleration due to gravity. Hence the graph looks like a straight line with positive slope. The first equation of motion verifies this.
Ques 14. In a uniformly accelerated motion, the speed varies from 0 to 20 m/s in 4 s. What is the average speed during the motion?
- 10 m/s
- 20 m/s
- 0 m/s
- 15 m/s
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Ans. (a) 10 m/s
Explanation: From first equation of motion,
v = u + at
Where, a = 5 m/s2.
From second equation of motion we have s = ut + (1/2)at2,
Where, s = 40 m.
Average speed = s/t = 40/4 = 10 m/s
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