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?
by 4
the state of rest or motion of a body is reiative.
To find the factor by which the car's kinetic energy increases when its speed is doubled, we need to compare the kinetic energy before and after the speed change.
The formula for kinetic energy is:
Kinetic Energy = 1/2 * mass * velocity^2
Since we are only concerned with the factor by which the kinetic energy increases, we can simply compare the squares of the velocities before and after the speed change.
1. Calculate the initial kinetic energy:
Kinetic Energy before = 1/2 * mass * (initial velocity)^2
2. Calculate the final kinetic energy:
Kinetic Energy after = 1/2 * mass * (final velocity)^2
3. Divide the final kinetic energy by the initial kinetic energy to find the factor:
Factor = (Kinetic Energy after) / (Kinetic Energy before)
Now let's plug in the values into the formula:
1. Initial kinetic energy:
Kinetic Energy before = 1/2 * mass * (10 m/s)^2
2. Final kinetic energy:
Kinetic Energy after = 1/2 * mass * (20 m/s)^2
3. Factor:
Factor = (1/2 * mass * (20 m/s)^2) / (1/2 * mass * (10 m/s)^2)
Notice that the mass cancels out, so we can simplify:
Factor = ((20 m/s)^2) / ((10 m/s)^2)
Now, let's calculate the factor:
Factor = (400 m^2/s^2) / (100 m^2/s^2)
Factor = 4
So, the car's kinetic energy increases by a factor of 4 when its speed is doubled.