Question

A car starts from rest and accelerates uniformly to a speed of 72 km. p.h. over a distance of 500 m. Calculate the time taken to attain the speed.

(a) 50 s

(b) 60 s

(c) 70 s

(d) 80 s

The question was posed to me in an interview for job.

My enquiry is from Numericals On Kinematics Of Motion topic in portion Kinematics & Kinetics of Motion of Machine Kinematics

Answer 1

Correct choice is (a) 50 s

For 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