Question

A 1000 kg car comes to a stop without skidding. The car's brakes do 50,000 J of work to stop the car. What was the initial velocity of the car?

a) 22 m/s
b) 14 m/s
c) 17 m/s
d) 10 m/s

Answer 1

The initial velocity of the 1000 kg car stopping with 50,000 J of work done by the brakes was 10 m/s, corresponding to option (d).

Step-by-step explanation:

To determine the initial velocity of the car, we can use the work-energy theorem. This principle states that the work done by the brakes in stopping the car is equal to the change in kinetic energy of the car. The formula to calculate the work done is:

Work done = Kinetic energy change = ½ * mass * velocity2

Given the mass of the car is 1000 kg and the work done by the brakes is 50,000 J, we can set up the following equation:

50,000 J = ½ * 1000 kg * velocity2

After simplifying, we find:

velocity2 = (2 * 50,000 J) / 1000 kg = 100 m2/s2

velocity = √100 m2/s2 = 10 m/s

Therefore, the initial velocity of the car was 10 m/s, which corresponds with option (d).