A car engine supplies constant power P while the car moves on a horizontal road against a resistive force kv². Its terminal speed is:
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Question

A car engine supplies constant power P while the car moves on a horizontal road against a resistive force kv². Its terminal speed is:

G1 Physics · Accepted Answer

At terminal speed acceleration is zero, so engine force equals kv². Since engine force=P/v, P/v=kv² ⇒ v³=P/k ⇒ v=(P/k)¹ᐟ³.