The velocity of a body depends on time according to the equation $v=\frac{t^2}{10}+20$. The body is undergoing

Draw the $x\to t$ graphs for positive, negative and zero acceleration.

If the velocity of a particle is $(10 + 2t^2) m/s$, then the average acceleration of the particle between $2s$ and $5s$ is..........$m/s^2$

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 $P$ ?

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:

Acceleration versus time graph of a body starting from rest is shown in the figure. The velocity versus time graph of the body is given by