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The DeLorean featured in the movie is an actual car, made by John DeLorean. He had originally envisioned the car would produce 200 horsepower, but eventually settled on 170 horsepower output for the engine. In the United States, the vehicles were required to have catalytic converters, causing a 40 horsepower reduction in output power. If the DeLorean requires 850 kilojoules to reach a speed of 60 miles per hour, how much longer does a US model take to reach 60 mph than its European counterpart?

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AMB000

Answer:

[tex]\Delta t=2s[/tex]

Explanation:

Power is by definition energy per unit time P=E/t, so the time it takes to provide an energy E at power P is t=E/P. We have the energy (E=8.5\times10^5J) and both powers,  ([tex]P_1[/tex]=170hp and [tex]P_2[/tex]=130hp, 40hp less than [tex]P_1[/tex]), which for converting to Watts we only need to multiply the power in hp by the conversion factor 745.7W/hp.

We can then calculate the difference between the times asked:

[tex]\Delta t=t_2-t_1=\frac{E}{P_2}-\frac{E}{P_1}=E( \frac{1}{P_2}-\frac{1}{P_1})[/tex]

Which for our values means:

[tex]\Delta t=E(\frac{1}{P_2}-\frac{1}{P_1})=(8.5\times10^{5}J)(\frac{1}{(130hp)(745.5W/hp)}-\frac{1}{(170hp)(745.5W/hp)})=2s[/tex]

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