Answer:
4. Slowing down from 100 km/h to 50 km/h
Step-by-step explanation:
The work done by car is given as the change in the kinetic energy of the car. Mathematically,
W = ΔK
where
W = work done by the brakes.
ΔK = Change in kinetic energy.
Kinetic Energy is given as:
[tex]K = \frac{1}{2}mv^{2}[/tex]
Case 1: The car goes from 50 km/h to 0 km/h
ΔK = [tex]K_{f} - K_{i}[/tex]
ΔK = [tex](\frac{1}{2}*50^{2}*m) - (\frac{1}{2}*0^{2}*m)[/tex]
ΔK = 1250m J
∴ W = 1250m J
Case 2: The car goes from 100 km/h to 50 km/h
ΔK = [tex]K_{f} - K_{i}[/tex]
ΔK = [tex](\frac{1}{2}*100^{2}*m) - (\frac{1}{2}*50^{2}*m)[/tex]
ΔK = 5000m - 1250m
ΔK = 3750m J
∴ W = 3750m J
Note: Mass of the car is constant.
Hence, slowing down from 100 km/h to 50 km/h requires the brakes to do more work, precisely 3 times more work [tex](3750m/1250m = 3)[/tex]
