The motion of a particle is described by the equation $x = a + bt^2$ where $a = 15 \, cm$ and $b = 3 \, cm/s^2$. Its instantaneous velocity at time $t = 3 \, s$ will be ........ $cm/s$.

The position $x$ of a particle with respect to time $t$ along the $x$-axis is given by $x = 9t^2 - t^3$,where $x$ is in metres and $t$ is in seconds. What will be the position of this particle when it achieves maximum speed along the $x$-direction?

For the given displacement-time graph,what will the corresponding velocity-time graph look like?

In the picture shown,a ball starting from rest rolls down a ramp $AB$,moves along the horizontal bottom $BC$,then goes up a smaller ramp $CD$,and thereafter rolls on the horizontal plane $DE$. Ignore friction and air resistance. Which of the following figures shows the variation in speed with time?

The speed-time graph of a particle moving along a fixed direction is shown in the figure. What is the average speed of the particle over the intervals: $(a)$ $t = 0\; s$ to $10\; s$,and $(b)$ $t = 2\; s$ to $6\; s$?

The diagram shows the variation of $1/v$ (where $v$ is the velocity of the particle) with respect to time $t$. Using the details given in the graph,the instantaneous acceleration at time $t = 3\,s$ will be equal to $...........\,m/s^2$.