The $x$ and $y$ coordinates of a particle at any time $t$ are given by $x = 7t + 4{t^2}$ and $y = 5t$, where $x$ and $y$ are in metre and $t$ in seconds. The acceleration of particle at $t = 5\;s$ is.........$m/{s^2}$

A car, starting from rest, accelerates at the rate $f$ through a distance $S$, then continues at constant speed for time $t$ and then decelerates at the rate $\frac{f}{2}$ to come to rest. If the total distance traversed is $15S$, then

Suggest a suitable physical situation for following graphs.

A particle initially at rest starts moving from reference point. $\mathrm{x}=0$ along $\mathrm{x}$-axis, with velocity $v$ that varies as $v=4 \sqrt{\mathrm{x} m} / \mathrm{s}$. The acceleration of the particle is __________$ \mathrm{ms}^{-2}$.

The velocity of a body depends on time according to the equation $v=\frac{t^2}{10}+20$. The body is undergoing

If the velocity $v$ of a particle moving along a straight line decreases linearly with its displacement $s$ from $20\,ms ^{-1}$ to a value approaching zero at $s=30\,m$, then acceleration of the particle at $s=15\,m$ is $........$