Displacement $(x)$ of a particle is related to time $(t)$ as:

$x = at + bt^2 -ct^3$

where $a, b$ and $c$ are constants of the motion. The velocity of the particle when its acceleration is zero is given by

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 $t=$

The acceleration-time graph of a body is shown below The most probable velocity-time graph of the body is

The velocity-time graphs of a car and a scooter are shown in the figure. $(i)$ the difference between the distance travelled by the car and the scooter in $15\, s$ and $(ii)$ the time at which the car will catch up with the scooter are, respectively

The velocity-time and acceleration-time graphs of a particle are given as Its position-time graph may be gvien as

A particle moves towards east with velocity $5\, m/s$. After $10$ seconds its direction changes towards north with same velocity. The average acceleration of the particle is