The figure shows a velocity-time graph of a particle moving along a straight line. The maximum displacement of the particle is ........ $m$.

The relation between velocity $v$ and displacement $x$ is $v = x^2$. Find the acceleration at $x = 3 \ m$.

The area under an acceleration-time graph gives:

The area $A$ of a blot of ink is growing such that after $t$ seconds its area is given by $A = (3t^2 + 7) \, cm^2$. Calculate the rate of increase of area at $t = 2 \, s$. .......... $cm^2/s$

If a steel ball is dropped from a height onto a marble floor,what will the velocity-time graph look like?

Two small blocks slide without losing contact with the surface along two frictionless tracks $1$ and $2$,starting at the same time with the same initial speed $v$. Track $1$ is perfectly horizontal,while track $2$ has a dip in the middle,as shown in the figure. Which block reaches the finish line first? [Hint: Use velocity-time graph to solve]