If the speed of the vehicle is doubled, what is the required increase in stopping power?

When the speed of a vehicle is doubled, the required stopping power increases by a factor of four. This is due to the physics of stopping distance and the formula for kinetic energy. The kinetic energy of a moving object is directly proportional to the square of its speed.

This means that if you double the speed of the vehicle, the kinetic energy (and therefore the energy that needs to be dissipated to bring the vehicle to a stop) increases by a factor of two squared. Specifically:

• If the original speed is ( v ), then the kinetic energy is proportional to ( v^2 ).
• When the speed is increased to ( 2v ), the new kinetic energy becomes ( (2v)^2 = 4v^2 ).

Thus, to stop the vehicle safely at the higher speed, the braking system must provide four times the stopping power to counteract the increased kinetic energy. This relationship highlights the critical importance of understanding speed and stopping distance in vehicle operation, especially when dealing with heavier loads or higher speeds where the increase in stopping power becomes even more paramount.