# A particle moving along x-axis has an acceleration f at time t, given by f = f0 (1 - 1/t), where f0 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

Given

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

At t = 0 and v = 0

When f = 0 then,

0 =

$$\begin{array}{l}f_{0}(1-\frac{t}{T})\end{array}$$

T = t ———— (1)

f = (final – initial velocity)/ Time

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

From equation (1)

We know that, T = t

$$\begin{array}{l}v=\frac{1}{2}f_{0}T\end{array}$$