Question

A car having a mass of 1000 Kg is moving at a speed of 30 m/sec. Brakes are applied to stop the car so that it comes to rest. If the frictional force between the tyres of the car and the road surface is 5000 N, the car will stop/comes to rest in

(A) 5 seconds
(B) 10 seconds
(C) 12 seconds
(D) 6 seconds

Answer 1

Hint:Use the first equation of motion and put all the required value from the question in that equation such as initial velocity given, final velocity will be zero as we have to stop the car, force and mass is given we can find the acceleration also and finally after putting all these we get the time required.


Formula used:
First equation of motion: $v = u + at$
Where, v is final velocity.
u is initial velocity.
a is acceleration.
And t is time.
Also, acceleration $a = \dfrac{F}{m}$


Complete answer:
Let start with the given information:
Initial velocity, $u = 30m/s$.
Final velocity, v = 0.
We know that: acceleration $a = \dfrac{{Force}}{{mass}} = \dfrac{F}{m}$
$a = - \dfrac{{5000}}{{1000}} = - 5m/{s^2}$
Now, from first equation of motion;
$v = u + at$
$0 = 30 + ( - 5t)$
By solving;
$t = 6\sec $
Therefore, the time required to stop the car is 6 seconds.

Hence, the correct answer is Option(D).


Note: Here the body given that is car needs to be stopped by applying brakes that’s why the final velocity is zero but it’s not the case all the time so be careful about the same and put the values accordingly from the information provided in the question. Also check the units before putting the values.