Final answer:
The force of impact increases as the square of the speed; hence, doubling the speed quadruples the impact force, and tripling the speed multiplies the force by nine.
Step-by-step explanation:
The force of impact in a crash is related to the kinetic energy of the vehicle, which in turn depends on the square of the vehicle's speed. Therefore, when you double the speed of a vehicle, its kinetic energy—and consequently, the force of impact—increases by a factor of four (speed squared). If you triple the vehicle's speed, the increase is by a factor of nine (three squared). This is because kinetic energy is given by the formula 1/2 mv², where m is the mass and v is the velocity (speed). In the options provided, (a) is therefore correct: Double your speed and the force of impact is 4 times greater, triple your speed and it becomes 9 times greater.