Question

A particle is moving with velocity 1/4*t(t^2+ 5t) then acceleration at time t is​

Answer 1

Dear student,

Given :-

• velocity at t, v = t³ + 5t²/4

To find :-

• acceleration a at t.

Solution :-

In order to derive acceleration from velocity, we know that we do differentiation. So, differentiating v with respect to t we obtain;

v = t³ + 5t²/4

dv/dt = d( t³ + 5t²/4)/dt

a = (dt³ + 5 dt²/4)/dt

a = 1/4 (3t² + 5(2t) ]

a = 1/4 (3t² + 10t)

a = 3t² + 10t/ 4 m/s²

Hence, the acceleration a at time t is 3t² + 10t/ 4 m/s² .