The velocity-time graphs of a car and a scooter are shown in the figure. $(i)$ The difference between the distance travelled by the car and the scooter in $15\, s$ and $(ii)$ the time at which the car will catch up with the scooter are,respectively:

The figure shows a speed-time graph of a particle in motion along a constant direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude? In which interval is the average speed greatest? Choosing the positive direction as the constant direction of motion,give the signs of $v$ and $a$ in the three intervals. What are the accelerations at the points $A, B, C$ and $D$?

The $v-t$ graphs of two moving objects make angles of $30^{\circ}$ and $45^{\circ}$ with the time axis. Find the ratio of their accelerations.

$A$ particle of mass $50 \, g$ moves on a straight line. The variation of speed with time is shown in the figure. Find the force acting on the particle at $t = 2, 4,$ and $6 \, s$.

The velocity $(v)$ versus time $(t)$ plot of a particle is shown in the figure, for a time interval of $40 \text{ s}$. The total distance travelled by the particle and the average velocity during this period are, respectively . . . . . . .

$A$ particle covers a distance from $A$ to $B$ over a period of time; the distance versus time plot is shown below. Then which of the following is true for the motion of the particle?