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 determine the factor by which the car's kinetic energy increases when its speed is doubled, we need to compare the kinetic energy at the initial speed to the kinetic energy at the final speed.
The formula for kinetic energy is given by:
Kinetic Energy = (1/2) * mass * speed^2
Since only the speed changes in this case, we can assume that the mass of the car remains constant.
Let's denote the initial speed as v1 (10 m/s) and the final speed as v2 (20 m/s).
The kinetic energy at the initial speed is:
KE1 = (1/2) * mass * v1^2
The kinetic energy at the final speed is:
KE2 = (1/2) * mass * v2^2
We can calculate the factor by which the kinetic energy increases by dividing the kinetic energy at the final speed by the kinetic energy at the initial speed:
Factor = KE2 / KE1 = [(1/2) * mass * v2^2] / [(1/2) * mass * v1^2]
Since the mass appears in both the numerator and denominator, it cancels out:
Factor = [v2^2] / [v1^2]
Plugging in the values, we have:
Factor = [20^2] / [10^2] = 400 / 100 = 4
Therefore, the factor by which the car's kinetic energy increases when its speed is doubled from 10 m/s to 20 m/s is 4.