Question

A particle starting with certain initial velocity and uniform acceleration covers a distance of 12 m in first 3 seconds and a distance of 30 m in next 3 seconds. The initial velocity of the particle is 

(a) 3 ms^–1 

(b) 2.5 ms^–1 

(c) 2 ms^–1 

(d) 1 ms^–1

Answer 1

Correct option (d) 1 ms^–1

Explanation:

Let u be the initial velocity that have to find and a be the uniform acceleration of the particle.

For t = 3s, distance travelled S = 12 m and 

for t = 3 + 3 = 6 s distance travelled Sc = 12 + 30 = 42m 

From, S = ut + 1/2 at²

12 = u x 3 + 1/2 x a x 3²

or 24 = 6u + 9a .....(i)

Similarly,  42 = u x 6 + 1/2 x a x 6²

or 42 = 6u + 18a .....(ii)

on solving, we get u = 1ms^-1