If the position-time graph of a particle is a sine curve as shown,what will be its velocity-time graph?

Explain instantaneous velocity and discuss how it can be determined from an $x-t$ graph.

The graph below shows the velocity versus time graph for a body. Which of the following graphs represents the corresponding acceleration $v/s$ time graph?

Among the following,the velocity $(v)$ - time $(t)$ graph representing the motion of a vertically projected body is

The velocity of a particle moving on the $x$-axis is given by $v = x^2 + x$,where $v$ is in $m/s$ and $x$ is in $m$. Find its acceleration in $m/s^2$ when passing through the point $x = 2 \ m$.

Consider a car initially at rest,starts to move along a straight road first with acceleration $5 \ m \ s^{-2}$,then with uniform velocity and finally,decelerating at $5 \ m \ s^{-2}$,before coming to a stop. Total time taken from start to end is $t = 25 \ s$. If the average velocity during that time is $72 \ km \ hr^{-1}$,the car moved with uniform velocity for a time of: (in $s$)