The displacement of a particle, moving in a straight line, is given by $s = 2{t^2} + 2t + 4$ where $s$ is in metres and $t$ in seconds. The acceleration of the particle is........$ms^{-2}$

An object with a mass $10 \,kg$ moves at a constant velocity of $10 \,m/sec$. A constant force then acts for $4\, second$ on the object and gives it a speed of $2\, m/sec$ in opposite direction. The acceleration produced in it, is ........ $m/{\sec ^2}$

Two points move in the same straight line starting at the same moment from the same point in it. The first moves with constant velocity $u$ and the second with constant acceleration $f$. During the time elapses before the second catches, the first greatest distance between the particle is $........$

The initial velocity of a particle moving along $x$-axis is $u$ (at $t=0$ and $x=0$ ) and its acceleration $a$ is given by $a=k x$. Which of the following equation is correct between its velocity $(v)$ and position $(x)$ ?

Velocity-time $(v-t)$ graph for a moving object is shown in the figure. Total displacement of the object during the time interval when there is non-zero acceleration and retardation is........$m$

A body starts from rest with an acceleration $a_{1},$ after two seconds another body $B$ starts from rest with an acceleration $a _{2}$. If they travel equal distance in fifth second, after the starts of $A$, the ratio $a _{1}: a _{2}$ will be equal to