The position $x$ of a particle varies with time $t$ as $x = a{t^2} - b{t^3}$. The acceleration of the particle will be zero at time $t$ equal to

A body is moving with a uniform acceleration covers $40\,m$ in the first $4\,s$ and $120\,m$ in next $4\,s.$ Its initial velocity and acceleration are

What is retardation ?

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.

Will the acceleration increase or decrease with increase in velocity ?

A particle moves along a straight line such that its displacement at any time $t$ is given by $s = (t^3 -3t^2 + 2)\,m$ The displacement when the acceleration becomes zero is........$m$