If you triple the speed of a car, by how many times does the force of impact increase?

When considering the relationship between speed and the force of impact during a collision, it’s important to refer to the physics of motion and energy. The kinetic energy of a vehicle, which contributes to the force of impact, is proportional to the square of its speed. This means that if the speed of the vehicle is tripled, the kinetic energy increases by the square of that factor.

Tripling the speed means calculating the increase as follows: If the original speed is 'v', then tripling it gives a new speed of '3v'. The kinetic energy at this new speed can be expressed as:

Kinetic Energy = (1/2) * mass * (speed)^2

When applying this to our scenario:

Original Kinetic Energy = (1/2) * m * v^2 New Kinetic Energy = (1/2) * m * (3v)^2 = (1/2) * m * 9v^2

Thus, when you compare the new kinetic energy (9 times the original kinetic energy) to the original, you find that the force of impact, which directly relates to kinetic energy at the moment of impact, increases by a factor of 9.

This understanding highlights why the correct answer