When driving twice the speed, by how many times does the impact force increase?

The impact force increases with the square of the speed due to the principles of physics related to kinetic energy and momentum. When an object's speed is doubled, its kinetic energy, which is a function of the square of its velocity, increases by a factor of four.

Kinetic energy can be described by the formula:

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

where ( KE ) is kinetic energy, ( m ) is mass, and ( v ) is velocity. If the velocity is doubled (2v), the new kinetic energy becomes:

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

This means that the kinetic energy—and consequently, the impact force—has increased by a factor of four when the speed is doubled. Therefore, the impact force increases four times when the driving speed is doubled, making that the correct choice.