Question

A car weighing 1000kg and travelling at 30m/s stops at a distance of 50m deaccelerating uniformly. What is the force exerted by the brakes? What is the work done by the brakes?

Answer 1

mass= 1000
initial velocity= u= 30
final velocity= v= 0
distance= s= 50
as we know 
v²= u²+ 2as
0²= 30² + 2 a 50
-900= 100a
a= -9

And F= ma
F= 1000 x -9
F= -9000N

W= Fs
W= -9000 x 50
= -450 KJ

Answer 2

Given that,

Mass of a car, m = 1000 kg

Speed of the car, u = 30 m/s

Distance, d = 50 m

To find,

The force exerted by the brakes and the work done by the brakes.

Solution,

As the car is deaccelerating uniformly, it means its final velocity will be 0. Let a is its acceleration. So,

$v^2-u^2=2ad\\\\a=\dfrac{-u^2}{2d}\\\\a=\dfrac{-(30)^2}{2\times 50}\\\\a=-9\ m/s^2$

Now the force exerted by the brakes is given by :

F = ma

$F=1000\times -9\\\\F=-9000\ N$

Work done is equal to : W = Fd

$W=-9000\times 50\\\\W=-450\ kJ$

Hence, this is the required solution.