A motorcycle of mass m starting from resst can attain a speed v after work w is performed by its engine. If the engine could perform work 4w then the final speed would be?

v' = 2 v

Explanation:

The work performed by the engine is equal to the change in the kinetic energy of the motorcycle.

w = ΔK = K₂ - K₁ = 1/2 × m × v₂² - 1/2 × m × v₁²

Since v₁ = 0 (rest), the work is equal to the final kinetic energy of the motorcycle. We will express this as:

w = 1/2 × m × v²  [1]

If the engine performed a new work w' = 4w, we get:

w' = 1/2 × m × v'²

4w = 1/2 × m × v'²

w = 1/8  × m × v'²  [2]

Since [1] = [2]

1/2 × m × v² = 1/8  × m × v'²

4 v² = v'²

v' = 2 v