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, we need to calculate the ratio of the final kinetic energy to the initial kinetic energy.
The formula for kinetic energy is:
Kinetic Energy = (1/2) * mass * velocity^2
Given that the car's speed is doubled from 10 m/s to 20 m/s, we can assume that the mass remains constant.
Let's start by calculating the initial kinetic energy:
Initial kinetic energy = (1/2) * mass * (initial velocity)^2
Initial kinetic energy = (1/2) * mass * (10 m/s)^2
Now, let's calculate the final kinetic energy:
Final kinetic energy = (1/2) * mass * (final velocity)^2
Final kinetic energy = (1/2) * mass * (20 m/s)^2
To find the factor by which the car's kinetic energy increases, we divide the final kinetic energy by the initial kinetic energy:
Factor = (Final kinetic energy) / (Initial kinetic energy)
Factor = [(1/2) * mass * (20 m/s)^2] / [(1/2) * mass * (10 m/s)^2]
Simplifying the equation:
Factor = (20 m/s)^2 / (10 m/s)^2
Factor = 400 / 100
Factor = 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.