$(a)$ Derive graphically the equation for velocity$-$time relation.
$(b)$ Name the device used to measure distance travelled by a vehicle.
$(c)$ Can displacement of a moving object be zero? Give reason.

(N/A) Consider a velocity$-$time graph where an object starts with initial velocity $u$ at time $t=0$ and reaches final velocity $v$ at time $t$. The slope of the velocity$-$time graph represents acceleration $(a)$.
Slope $= \frac{\text{Change in velocity}}{\text{Time taken}} = \frac{v - u}{t}$.
Therefore,$a = \frac{v - u}{t}$,which gives $at = v - u$,or $v = u + at$.
$(b)$ The device used to measure the distance travelled by a vehicle is called an odometer.
$(c)$ Yes,the displacement of a moving object can be zero. This happens if the object returns to its initial starting position after completing its motion,as displacement is the shortest distance between the initial and final positions.