Question

A car moving at 50 km/hr skids 20 m with locked brakes. how far will the car skid with locked brakes if it were traveling at 150 km/hr?

Answer 1

The energy to be dissipated is proportional to 1/2 m v^2 ie proportional to v^2 for the same car 

In turn F * d = work done. 
F is constant ( same brakes) 
so d is proportional to v^2 
if v is multiplied by 3 then d is multiplied by 3^2 = 9 
distance = 180m

Answer 2

Answer:

If the car is travelling at 150 km/hr it will travel 180.12 m before stopping.

Explanation:

Here for the first condition

     Initial speed, u = 50 km/hr = 13.89 m/s

     Distance, s = 20 m

     Final speed, v = 0 m/s

     We have equation of motion, v² = u²+2as

      0² = 13.89²+2 x a x 20

       a = -4.82 m/s²

Deceleration of car brake = 4.82 m/s²

For the second condition

      Initial speed, u = 150 km/hr = 41.67 m/s

      Final speed, v = 0 m/s

      Acceleration, a = -4.82 m/s²        

     We have equation of motion, v² = u²+2as

      0² = 41.67²-2 x 4.82 x s

       s = 180.12 m

If the car is travelling at 150 km/hr it will travel 180.12 m before stopping.