If you double the speed of a car, how much does the kinetic energy increase?
How do you know?
KE = 1/2 mv^2
replace v with 2v and you get
1/2 m(2v)^2 = 1/2 m * 4v^2 = 4(1/2 mv^2) = 4*KE
If you multiply the speed by n, you get n^2 times the KE
To determine how much the kinetic energy of a car increases when its speed is doubled, we can use the equation for kinetic energy:
Kinetic Energy = 1/2 * mass * velocity^2
When we double the speed of the car, the new velocity will be two times the original velocity (2v). Let's assume the mass of the car remains constant.
To find out how much the kinetic energy increases, we can compare the initial kinetic energy (KE1) to the final kinetic energy (KE2) by plugging the respective velocities into the equation:
KE1 = 1/2 * mass * velocity^2
KE2 = 1/2 * mass * (2v)^2
Now let's compare the two kinetic energies:
KE2/KE1 = [1/2 * mass * (2v)^2] / [1/2 * mass * velocity^2]
= (1/2 * mass * 4v^2) / (1/2 * mass * v^2)
= 4v^2 / v^2
= 4
Thus, when we double the speed of the car, the kinetic energy increases by a factor of 4 or 400%.