Question

A car starts from rest and accelerates uniformly to a speed of 72 km. p.h. over a distance of 500 m. If a further acceleration raises the speed to 90 km. p.h. in 10 seconds, find this acceleration and the further distance moved.

(a) 0.3 m/s^2

(b) 0.4 m/s^2

(c) 0.5 m/s^2

(d) 0.6 m/s^2

This question was posed to me in an online interview.

This interesting question is from Numericals On Kinematics Of Motion topic in division Kinematics & Kinetics of Motion of Machine Kinematics

Answer 1

Right answer is (c) 0.5 m/s^2

The explanation: Given : u = 0 ; v = 72 km. p.h. = 20 m/s ; s = 500 m

First of all, let us consider the motion of the car from rest.

Acceleration of the car

Let a = Acceleration of the car.

We know that

v^2 = u^2 + 2as

or, 20^2 = 0 + 2a x 500 = 1000a

or, a = 20^2/1000 = 0.4 m/s^2

Let t = Time taken by the car to attain the speed.

We know that v = u + a.t

∴ 20 = 0 + 0.4 × t or t = 20/0.4 = 50 s

Now consider the motion of the car from 72 km.p.h. to 90 km.p.h. in 10 seconds.

Given : Initial velocity, u = 72 km.p.h. = 20 m/s ;

Final velocity, v = 96 km.p.h. = 25 m/s ; t = 10 s

Let a = Acceleration of the car.

We know that v = u + a.t

25 = 20 + a × 10 or a = (25 – 20)/10 = 0.5 m^2