Question

A car travels from rest with a constant acceleration ${}^{\prime }{a}^{\prime }$ for $t$ seconds. What is the average speed of the car for its journey, if the car moves along a straight road ?

• A. $v=\frac{a{t}^2}{2}$
• B. $v=2a{t}^2$
• C. $v=\frac{at}{2}$
• D. None

Answer 1

Answer: (C)

$v=\frac{at}{2}$

Initial speed of car $u=0$
Distance covered by car in $t$ seconds is given by second equation of motion,

$S=ut+\frac{1}{2}a{t}^2$
$⟹S=\frac{1}{2}a{t}^2$ $(\because u=0)$

Average speed of car = $\frac{\text{total distance}}{\text{total time}}$

$v_{avg}=\frac{S}{t}=\frac{\frac{1}{2}a{t}^2}{t}=\frac{at}{2}$

So option C is correct.