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

When considering how the force exerted by a vehicle changes with speed, we must refer to the principles of physics, specifically the relationship between kinetic energy and velocity. The force exerted by a vehicle in a collision or similar scenarios is directly related to its kinetic energy, which is calculated using the formula ( KE = \frac{1}{2} mv^2 ), where ( m ) is the mass of the vehicle and ( v ) is its velocity.

If the speed of the vehicle is doubled, this affects the velocity term in the kinetic energy equation. Specifically, if the velocity is increased from ( v ) to ( 2v ), the kinetic energy becomes:

[

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

]

This means that doubling the speed results in the kinetic energy increasing by a factor of four. In scenarios where force is a consideration—such as in impacts or collisions—the force exerted is proportional to the change in kinetic energy over time. Thus, when the speed is doubled, the force exert