Question

A race car is moving on a straight road with a speed of $180km{h}^{-1}$. If the driver stops the car in $25$ s by applying the brakes, calculate the distance covered by the car during the time brakes are applied. Assume the acceleration of the car is uniform throughout the retarding motion.

Answer 1

Given,

Initial speed $u=180km/h$

$u=\frac{180\times 1000}{3600}=50m/s$

Final velocity, $v=0$

Time taken, $t=25s$

Acceleration, $a$

Distance covered, $s$

Using Newton's first equation of motion,

$v=u+at$

$⟹a=\frac{v-u}{t}$

$a=\frac{0-50}{25}$

$a=-2m/s^2$

Using Newton's second equation of motion,

$s=ut+\frac{1}{2}a{t}^2$

$s=(50\times 25)+\frac{1}{2}(-2)(25{)}^2$

$s=625m$