A car is accelerated by a constant force, F. The distance required to accelerate the car from rest to the speed v is Δx.

(a) Is the distance required to accelerate the car from the speed v to the speed 2v equal to Δx, 2Δx, 3Δx, or 4Δx?

(b) Choose the best explanation from among the following:

I. The final speed is twice the initial speed.

II. The increase in speed is the same in each case.

III. Work is force times distance, and work depends on the speed squared.