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

The relation between time ' $t$ ' and distance ' $x$ ' is $t=$ $\alpha x^2+\beta x$, where $\alpha$ and $\beta$ are constants. The relation between acceleration $(a)$ and velocity $(v)$ is:

A train moves from one station to another in $2$ hours time. Its speed-time graph during this motion is shown in the figure. The maximum acceleration during the journey is.............$km\, h^{-2}$

A dancer moves counterclockwise at constant speed around the path shown below. The path is such that the lengths of its segments, $PQ, QR, RS$, and $SP$, are equal. Arcs $QR$ and $SP$ are semicircles. Which of the following best represents the magnitude of the dancer’s acceleration as a function of time $t$ during one trip around the path, beginning at point $P$ ?

Define acceleration , average acceleration and instantaneous acceleration.

The displacement is given by $x = 2{t^2} + t + 5$, the acceleration at $t = 2\;s$ is.........$m/{s^2}$