Doubling the speed of a vehicle will increase the force exerted by that vehicle by a factor of?

When considering the relationship between the speed of a vehicle and the force it can exert, particularly in the context of impact or momentum, it is important to understand the physics involved. The kinetic energy of a vehicle, which is related to the force exerted during a collision, is calculated using the formula KE = 1/2 mv², where 'm' is mass and 'v' is velocity.

As speed doubles, the velocity component in the formula is squared. This means that if the speed (v) is increased from v to 2v, the new kinetic energy would be KE = 1/2 m(2v)² = 1/2 m(4v²), which results in four times the original kinetic energy (and thus, the force exerted during a collision).

This principle reflects how increasing speed has a quadratic effect on the force exerted by the vehicle. Therefore, when speed is doubled, the force exerted increases by a factor of four, which aligns with the selection of the fourth answer option. This is a critical concept in understanding vehicle dynamics and the potential hazards associated with increased braking distances and the severity of collisions.