# A particle moving along x-axis has an acceleration f at time t, given by $f = f_{0}(1-\frac{t}{T})$, where $f_{0}$ and T are constants. The particle at T = 0 has zero velocity. In the time interval between t = 0 and the instant when f = 0, the velocity (va) of the particle is then:(a) $\frac{1}{2}f_{0}T$(b) $f_{0}T$(c) $\frac{1}{2}f_{0}T^{2}$(d) $f_{0}T^{2}$

Given

$f = f_{0}(1-\frac{t}{T})$ where $f_{0}$ and T are constants

At t = 0 and v = 0

When f = 0 then,

0 = $f_{0}(1-\frac{t}{T})$

T = t ———— (1)

f = (final – initial velocity)/ Time

$\frac{dv}{dt}=f_{0}(1-\frac{t}{T})$ $\int dv=\int f_{0}(1-\frac{t}{T})dt$ $v=f_{0}(t-\frac{^{t^{2}}}{2T})$

From equation (1)

We know that, T = t

$v=\frac{1}{2}f_{0}T$

Therefore, the correct answer is option (a)

0 (0)

Upvote (0)

#### Choose An Option That Best Describes Your Problem

Thank you. Your Feedback will Help us Serve you better.