If a vehicle's speed doubles from 20 mph to 40 mph, the distance needed to stop the vehicle increases by ____ times.

If a vehicle's speed doubles from 20 mph to 40 mph, the distance needed to stop the vehicle increases by ____ times.

• A. 2
• B. 3
• C. 4
• D. 8

Answer: (C)

Stopping distance grows with speed when braking force stays the same, because braking distance is proportional to the square of speed. The braking distance is given by d = v^2/(2a). If you double the speed from 20 mph to 40 mph, the braking distance becomes (40)^2/(2a), which is four times longer than the original (20)^2/(2a). So the distance needed to stop increases by four times. This conclusion assumes you’re focusing on braking distance with constant deceleration; reaction distance, which depends linearly on speed, isn’t the focus here.

Stopping distance grows with speed when braking force stays the same, because braking distance is proportional to the square of speed. The braking distance is given by d = v^2/(2a). If you double the speed from 20 mph to 40 mph, the braking distance becomes (40)^2/(2a), which is four times longer than the original (20)^2/(2a). So the distance needed to stop increases by four times. This conclusion assumes you’re focusing on braking distance with constant deceleration; reaction distance, which depends linearly on speed, isn’t the focus here.