Question

A car and a bike with the same kinetic energy are brought to rest by the application of brakes

Answer 1

So,if a car and a bike with the same kinetic energy are brought to rest by the application of brakes.

The break of the car has to apply greater force than the break of the bike.

Because,the mass of the car is surely greater than the bike.That's why the bike gains more momentum than the car.

And more the momentum gained by the vehicle,the more the effort is needed by it's brake,in order to stop that particular vehicle.

Answer 2

"The formula for kinetic energy is given as $\frac{1}{2} mv^2$

As we know that the car would possess more mass than the bike and it is also given that the kinetic energy of car and bike are the same.  

So we can confirm that the velocity of car would be less than that of the bike

It is also given that the retarding forces are equal. So the vehicle moving with the lesser velocity would be stopped quicker and within a short distance. Hence the car would come to rest within a shorter distance after the brakes are applied."