In case one, a car speeds up from zero m/s to 15 m/s. In case two, the same car speeds up from 15 m/s to 30 m/s. The mass of the car is 1000 kg. Compare the energy needed to provide the increase in speed in each case. Give your answers in joules.

The energy needed to provide the increase in speed in the second case is Three times the energy needed to provide increase in speed in the first case.

Explanation:

For case one:

The energy needed for to provide the increase in speed = change in kinetic energy of the car

ΔEk = 1/2mv²- 1/2mu²...................... Equation 1

Where m = mass of the car, v = Final velocity of the car, initial velocity of the car

Given: m = 1000 kg, v = 15 m/s, u = 0 m/s

Substitute into equation 1

ΔEk = 1/2(1000)(15²)- 1/2(1000)(0²)

ΔEk = 112500 J.

For case Two,

Similarly,

ΔEk' = 1/2mv²-1/2mu²...................... Equation 2

Given: m = 1000 kg, v = 30 m/s, u = 15 m/s

ΔEk' = 1/2(1000)(30²)- 1/2(1000)(15²)

ΔEk' = 450000-112500

ΔEk' = 337500 J.

Comparing case one and case two above,

ΔEk' > ΔEk

ΔEk' = 3 ΔEk

Therefore the energy needed to provide the increase in speed in the second case is Three times the energy needed to provide increase in speed in the first case.