A car is traveling at 10 m/s. By what factor does the car's kinetic energy increase if its speed is doubled to 20 m/s?
To find the factor by which the car's kinetic energy increases, we need to compare the initial kinetic energy (when the car's speed is 10 m/s) to the final kinetic energy (when the car's speed is doubled to 20 m/s).
The formula for calculating kinetic energy is:
Kinetic energy = 0.5 * mass * velocity^2
In this case, we are not given the mass of the car, but we can ignore it for now since we are only interested in comparing the initial and final kinetic energies. Therefore, we can assume the mass remains constant in this scenario.
So, let's calculate the initial kinetic energy:
Initial kinetic energy = 0.5 * mass * (initial velocity)^2
= 0.5 * mass * (10 m/s)^2
= 0.5 * 100 * mass (since (10 m/s)^2 = 100 m^2/s^2)
Now, let's calculate the final kinetic energy (after doubling the speed):
Final kinetic energy = 0.5 * mass * (final velocity)^2
= 0.5 * mass * (20 m/s)^2
= 0.5 * 400 * mass (since (20 m/s)^2 = 400 m^2/s^2)
To find the factor by which the kinetic energy increases, we divide the final kinetic energy by the initial kinetic energy:
Factor = Final kinetic energy / Initial kinetic energy
= (0.5 * 400 * mass) / (0.5 * 100 * mass)
= 400 / 100
= 4
Therefore, the car's kinetic energy increases by a factor of 4 when its speed is doubled from 10 m/s to 20 m/s.
KE = 0.5m*V^2.
KE2/KE! = 0.5m(20)^2/0.5m*(10)^2 = 4.
Note: 0.5m cancels