How can you find the following ?
$(i)$ Velocity from a displacement$-$time graph.
$(ii)$ Acceleration from velocity$-$time graph.
$(iii)$ Displacement from velocity$-$time graph.
$(iv)$ Velocity from acceleration$-$time graph.
$(i)$ By finding the slope of graph, i.e.,
$v=\frac{\text { change in displacement }}{\text { time }}$
$(ii)$ By finding the slope of graph, i.e.
$v=\frac{\text { change in velocity }}{\text { time }}$
$(iii)$ By finding area under the graph line, i.e., $S=\Delta v \times \Delta t=$ change in velocity $\times$ change in time.
$(iv)$ By finding area under the graph line, i.e., $S=\Delta v \times \Delta t=$ change in velocity $\times$ change in time.
In a long distance race, the athletes were expected to take four rounds of the track such that the line of finish was same as the line of start. Suppose the length of the track was $200\, m$.
$(a)$ What is the total distance to be covered by the athletes ?
$(b)$ What is the displacement of the athletes when they touch the finish line ?
$(c)$ Is the motion of the athletes uniform or nonuniform ?
$(d)$ Is the displacement of an athlete and the distance moved by him at the end of the race equal ?
Give an expression for the speed of an athlete if he takes time $'t^{\prime}$ to go around a circular track, of radius ${ }^{\prime} r^{\prime}$
Starting from rest a scooter acquires a velocity of $36\, km h^{-1}$ in $10 \,s$ and then brakes are applied it takes $20\, s$ to stop. Calculate acceleration and distance travelled.
Can the distance travelled by a particle be zero when displacement is not zero ?
A cheetah can accelerate from rest at the rate of $4 m s^{-2}$
$(i)$ What will be the velocity attained by it in $10\, s$ ?
$(ii)$ How far will it travel in this duration ?