How many times greater is the force of collision if the driving speed is doubled?

When analyzing the force of collision related to driving speed, the relationship is governed by the physics of momentum and kinetic energy. Specifically, the force of a collision increases with the square of the speed. Kinetic energy, which is the energy that a vehicle possesses due to its motion, is calculated using the formula:

[ KE = \frac{1}{2} mv^2 ]

where ( m ) is mass and ( v ) is velocity. If the driving speed is doubled, the new velocity is ( 2v ). Plugging this into the kinetic energy formula gives:

[ KE' = \frac{1}{2} m (2v)^2 = \frac{1}{2} m (4v^2) = 4 \times \frac{1}{2} mv^2 = 4KE ]

This indicates that the kinetic energy—and consequently the impact force during a collision—is four times greater when the speed is doubled. Thus, the answer that states the force of collision is four times as great when the driving speed is doubled is correct. This relationship highlights the importance of speed management and its direct implications on safety in driving scenarios.