Motion NCERT Problems with Solutions- Part 2
Motion is a very important topic of Physics. Here are Motion NCERT Problems with Solutions for your practice
Problem 1. A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3.0 m s-2 for 8.0 s . How far does the boat travel during this time?
Problem 2. Fig. shows the distance-time graph of three objects A, B and C. Study the graph and answer the following questions:
Which of the three is traveling the fastest?
Are all three ever at the same point on the road?
How far has C traveled when B passes A?
How far has B traveled by the time it passes C?
(ii) No, all three do not meet at any point on the road,
(iii) When B passes A at point N (at 1.2 hours), C is at a distance of approximately 8 km from
the origin O.
(iv) B passes C at 0.7 hours. During this time B covers distance of 6 km.
Problem 3. A ball is gently dropped from a height of 20 m. If its velocity increases uniformly at the rate of 10 ms-2, with what velocity will it strike the ground? After what time will it strike the ground?
Problem 4. The speed-time graph for a car is shown is Fig.
(a) Find how far does the car travel in the first 4 seconds. Shade the area on the graph that represents the distance traveled by the car during the period.
(b) Which part of the graph represents uniform motion of the car?
(a) On horizontal axis, 5 small divisions = 2 s On vertical axis, 3 small divisions = 2 m/s
Area of 15 small squares
= 2 s x 2 m/s = 4m
Area of 1 small square =4/15m
Total area under the speed-time graph from time 0 to 4 s
= 57 small squares + 1/2 x 6 small squares
= 60 small square
Distance traveled by the car in first 4 seconds
= Area under the speed-time graph from 0 to 4 s
= 60 small squares
= 60 x 4/15 m
= 16 meter.
(b) After 6 s, the car has a uniform motion for straight part of graph BC.
Problem 5. State which of the following situations are possible and give an example for each of these:
(a) an object with a constant acceleration but with zero velocity.
(b) an object moving in a certain direction with an acceleration in the perpendicular direction.
(a) Yes, a body can have acceleration even if its velocity is zero. When a body is thrown
up, at highest point its velocity is zero but it has acceleration equal to acceleration due to gravity.
(b) Yes, when an object moves on a circular path, it has centripetal acceleration which is perpendicular to displacement.
Problem 6. An artificial satellite is moving in a circular orbit of radius 42250 km. Calculate its speed if it takes 24 hours to revolve around the earth.
Motion – Solved Problems
Problem 1. A car covers the 1st half of the distance between two places at a speed of 40 km/hr and the 2nd half at 60 km/hr what is the average speed of the car ?
Suppose the total distance covered is S. Then time taken to cover first’s distance with speed
Problem 2. An object moving to the right has a decrease in velocity from 5.0 m/s to 1.0 m/s in 2.0 s. What is the average acceleration ? What does your result mean ?
Given v0 = + 5.0 m/s, v = + 1.0 m/s, t = 2.0 s
According to the definition of average acceleration,
The negative sign means the acceleration is opposite to velocity (deceleration). The result means that the object decreases its velocity by 2.0 m/s every s or 2.0 m/s2.
Problem 3. The table below shows the distance in cm, travelled by the objects A, B and C during each second.
(i) Which object is moving with constant speed ? Give a reason for your answer.
(ii) Which object is moving with a constant acceleration ? Give a reason.
(iii) Which object is moving with irregular acceleration ?
The object A is moving with constant speed. The reason is that it covers equal distance=20cm. in each second,
The object C is moving with a constant acceleration. The reason is that for the object C, the distance covered increases by the same amount in each second. It can further be verified by drawing graph between S (total distance covered) and t2 (square of time taken). The graph will be a straight line.
The object B is moving with irregular acceleration.
Question 4. An automobile accelerates uniformly from rest to 25 m/s while traveling 100m. What is the acceleration of the automobile ?
Given: v0 = 0 (rest), v = 25m/s, x = 100m. Find a.
Since v2 = v02 + 2ax,
Since a is positive, it is in the direction of the velocity or motion.
Problem 5. car is moving at a speed 50 km/h. Two seconds there after it is moving at 60 km/h. Calculate the acceleration of the car.
Problem 6. A bus moving with a velocity of 60 km/h is brought to rest in 20 seconds by applying brakes. Find its acceleration.
Problem 7. A bullet moving with 10 m/s hits the wooden plank the bullet is stopped when it penetrates the plank 20 cm. deep, calculate retardation of the bullet.
Problem 8. A body with an initial velocity of 18 km/hr accelerates uniformly at the rate of 9 cm s-2 over a distance of 200m. Calculate:
(i) the acceleration in ms-2
(ii) its final velocity in ms-1
Problem 9. The graph represents the velocity of a particle as a function of time.
(a) What is the acceleration at 1.0 s ?
(b) What is the acceleration at 3.0 s ?
(c) What is the average acceleration between 0 and 5.0 s ?
(d) What is the average acceleration for the 8.0 s interval ?
(e) What is the displacement for the 8.0 s interval ?
The slope of the line is zero and a = 0.