Question

A car moving along a straight highway at a speed of $126km/hr$ is brought to a stop within a distance of $200m$. What is the retardation of the car (assumed uniform) and how long does it take for the car to stop?

Answer 1

Change unit of given speed from $km/hr\text{to}m/s$.
Initial velocity of the car
$u=126km/hr\Rightarrow u=126\times \left(1000/3600\right)=35m/s$

Use Newton's third equation of motion.
Given distance travelled by car before it comes to rest$\left(s\right)=200m$
Final velocity of the car$(v=0(\text{since it is at rest}\left)\right)$
Using $3rd$ equation of motion, $v^2=u^2+2as$
$a=(v^2-u^2)/2s$
$a=(0^2-35{)}^2/(2\times 200)$
$a=-3.06m/s^2$
Retardation of the car is $3.06m/s^2$

Use Newton's First equation of motion.
Let's assume the time taken by the car to stop as $tsec$
Using $1st$ equation of motion, $v=u+at$
$0=35-3.06t$
$t=35/3.06=11.43sec$
The car will take $11.43sec$ to stop.


Final Answer: Retardation of the car is $3.06m/s^2$
and it will take $11.43sec$ to stop.