Mark the correct statements for a particle going on a straight line
if the position and velocity have opposite sign, the particle is moving towards the origin
if the velocity is zero for a time interval, the acceleration is zero at any instant within the time interval
if the velocity and acceleration have opposite sign, the object is slowing down
All of the above
The $v - t$ graph of a moving object is given in figure. The maximum acceleration is...........$\mathrm{cm/sec}^{2}$
The velocity- displacement graph of a particle is shown in figure.
$(a)$ Write the relation between $v$ and $x$.
$(b)$ Obtain the relation between acceleration and displacement and plot it.
The velocity $v$ of a body moving along a straight line varies with time $t$ as $v=2 t^2 e^{-t}$, where $v$ is in $m / s$ and $t$ is in second. The acceleration of body is zero at $t=$
A car accelerates from rest at a constant rate $\alpha $ for some time, after which it decelerates at a constant rate $\beta $ and comes to rest. If the total time elapsed is $t$, then the maximum velocity acquired by the car is