A particle moving along $X$-axis has acceleration $f$ at time $t$ given by $f=f_0\left(1-\frac{t}{T}\right)$, 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 particle's velocity is

A particle is moving along the $Y$-axis. The position of the particle from the origin as a function of time $(t)$ is given as $y(t)=10 t e^{-2 t}$. How far is the particle from the origin when it stops momentarily? ( $y$ is given in units of metre and $t$ is in units of second)

A car travelling at $15 \mathrm{~m} / \mathrm{s}$ overtake another car travelling at $10 \mathrm{~m} / \mathrm{s}$. Assuming, each car is 4 m long. What is the time taken during the overtake?