The displacement $x$ of a particle along a straight line at time $t$ is given by $x = a_0 + a_1t + a_2t^2$. The acceleration of the particle is

$A$ particle initially at rest moves along the $x$-axis. Its acceleration varies with time as $a = 4t$. If it starts from the origin,the distance covered by it in $3 \ s$ is $........... \ m$.

$A$ particle is moving with constant acceleration $a$. The following graph shows the $v^{2}$ versus $x$ (displacement) plot. The acceleration of the particle is $...... \text{m/s}^{2}$.

$A$ motor car moving with a uniform speed of $20\,m/s$ comes to a stop on the application of brakes after travelling a distance of $10\,m$. Its acceleration is .......... $m/s^2$.

$A$ body starts from rest and moves with a uniform acceleration. The ratio of the distance covered by the body in the $n^{\text{th}}$ second of its motion to the total distance travelled in $n$ seconds is

If $x \propto t^{5/2}$,then