$A$ particle starts from the origin at time $t = 0$ and moves along the positive $x-$ axis. The velocity-time graph is shown in the figure. What is the position of the particle at time $t = 5\,s$ (in $,m$)?

$A$ particle of mass $m$ is constrained to move on the $x$-axis. $A$ force $F$ acts on the particle. $F$ always points toward the position labeled $E$. For example,when the particle is to the left of $E$,$F$ points to the right. The magnitude of $F$ is constant except at point $E$ where it is zero. The system is horizontal. $F$ is the net force acting on the particle. The particle is displaced a distance $A$ towards the left from the equilibrium position $E$ and released from rest at $t=0$. The velocity-time graph of the particle is:

The displacement-time graphs of two moving particles make angles of $30^{\circ}$ and $45^{\circ}$ with the time axis. The ratio of their velocities is

Between two stations,a train accelerates uniformly at first,then moves with constant velocity,and finally retards uniformly. If the ratio of the time taken is $1 : 8 : 1$ and the maximum speed attained is $60\,km/h,$ what is the average speed over the whole journey in $km/h$?

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

For the following velocity-time graph, the average speed for the motion during first $80 \, s$ is