Question

16. A particle moving along x-axis has acceleration f,
at time t, given f=for[1-t/T]
where f, and T are
constants. The particle at t = 0 has zero velocity.
When f = 0, the particle's velocity (V) is
[AIPMT (Prelims)-2007]​

Answer 1

1st begin with the definition of average velocity <V> = Total Displacement /Total time

Displacement as a function of time can be calculated by integrating the given expression of acceleration twice i.e.

A= ao (1-t/To)=dv/dt

Integrating we get :

V= ao (t-t^2/2To)=ds/dt

Again integrating we get:

S= ao (t^2 /2 - t^3/6To)

So, Average velocity :

<V>=S/t=ao (t/2 - t^2/6To)