An object starts a linear motion with velocity $u$ and with uniform acceleration $a$,it acquires a velocity $v$ in time $t$.
$(a)$ Draw its velocity-time graph.
$(b)$ Obtain the first equation of motion,$v = u + at$,for the velocity-time relation by using the velocity-time graph.
$(c)$ $A$ body moving with a velocity of $2 \, m s^{-1}$ acquires a velocity of $10 \, m s^{-1}$ in $5 \, s$. Find its acceleration.

(N/A) The velocity-time graph is shown in the figure.
$(b)$ The slope of the velocity-time graph gives the acceleration of the motion.
Slope $= \frac{\text{Change in velocity}}{\text{Time taken}} = \frac{v - u}{t - 0} = \frac{v - u}{t}$
Since acceleration $a = \text{slope}$,we have $a = \frac{v - u}{t}$.
Rearranging this gives $at = v - u$,or $v = u + at$.
$(c)$ Given:
Initial velocity $u = 2 \, m s^{-1}$
Final velocity $v = 10 \, m s^{-1}$
Time $t = 5 \, s$
Using the first equation of motion $v = u + at$:
$10 = 2 + a(5)$
$10 - 2 = 5a$
$8 = 5a$
$a = \frac{8}{5} = 1.6 \, m s^{-2}$
Thus,the acceleration is $1.6 \, m s^{-2}$.