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.