A car moving with a velocity of $10 \,m/s$ can be stopped by the application of a constant force $F$ in a distance of $20\, m$. If the velocity of the car is $30\, m/s$, it can be stopped by this force in......$m$

A point moves in a straight line so that its displacement $x\,m$ at time $t\,sec$ is given by $x^2 = 1 + t^2$. Its acceleration in $m/sec^2$ at a time $t\,sec$ is

Two trains travelling on the same track are approaching each other with equal speeds of $40\, m/s$. The drivers of the trains begin to decelerate simultaneously when they are just $2.0\, km$ apart. Assuming the decelerations to be uniform and equal, the value of the deceleration to barely avoid collision should be.........$m/{s^2}$

The velocity- displacement graph of a particle is shown in figure.

$(a)$ Write the relation between $v$ and $x$.

$(b)$ Obtain the relation between acceleration and displacement and plot it.

The velocity $(v)$ of a particle moving along $x$-axis varies with its position $x$ as shown in figure. The acceleration $(a)$ of particle varies with position $(x)$ as

For the velocity-time graph shown in the figure, in a time interval from $t=0$ to $t=6\,s$, match the following columns.