Consider that a truck is moving initially with $54 \mathrm{~km} / \mathrm{h}$. It has stopped by the driver after looking at an obstacle with a deceleration of $10 \mathrm{~m} / \mathrm{s}^2$. The distance travelled by truck before coming to rest is

A ball is thrown vertically upwards with an initial velcoity $u$ reaches maximum height in 5 s . The ratio of distance travelled by the ball in the 2nd and 7th second is (assume, $g=10 \mathrm{~m} / \mathrm{s}^2$ )

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)