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 ?

Solution.

Suppose the total distance covered is S. Then time taken to cover first’s distance with speed

40 km/hr.

 

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 ?

Solution.

Given v₀ = + 5.0 m/s, v = + 1.0 m/s, t = 2.0 s

Find

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 ?

Solution

Answer (i).

The object A is moving with constant speed. The reason is that it covers equal distance=20cm. in each second,

Answer (ii).

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.

t2	1	4	9	16	25
s	20	80	180	320	500

Answer (iii).

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 ?

Solution.

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.

Solution.

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.

Solution.

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.

Solution.

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

 

Solution. (i)

 

Solution (ii)

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 ?

Solution. (a)

 

Solution (b)

The slope of the line is zero and a = 0.

Solution (c)

 

Solution (d)

 

Solution (e)