Question

when brakes are applied to a car moving with a velocity of 54 km^-1 it comes to rest within 2 metre. calculate the frictional resistance if mass of the car is 150 kg

please solve

Answer 1

With the given data, one can easily calculate the value of retardation of the car by using the equation of motion:

v^2 - u^2 = 2as

where

'v' is the final velocity of the car which is 0 (because the car comes to a halt after applying the brakes)

'u' is the initial velocity of the car which is 
10 m/s

'a' is the retardation which is to be determined

's' is the distance the car treads after applying the brakes and coming to a halt, which is 20 m

Thus, the retardation comes out to be 
2.5 m/s^2

Now, we know that 
Force = Mass x Acceleration

Assuming the mass of the car to be M kg, the stopping force comes out to be 2.5M Newtons

Now if this force were to stop the same car travelling at 30 m/s, it would produce the same retardation as it did earlier, because the mass of the car is unchanged.

Now, u = 30 m/s instead of 10 m/s
Using the same equation 
v^2 - u^2 = 2as
The stopping distance 's' comes out to be

180 m

The lesson to learn here is that if your car stops in 80 feet doing 80 km/hr does not mean it will stop in 100 feet doing doing 100 km/hr. This is the reason why road authorities hesitate to increase speed limits even by humble amounts!