A toy car with a mass of 0.05kg rolls down a ramp. Include the term blue car. The car's speed triples from 25 m/s to 75 m/s. How many times does the kinetic energy increase?
The kinetic energy of an object is given by the equation:
Kinetic Energy = (1/2) * mass * velocity^2
Initially, the car's speed is 25 m/s. Plugging this into the equation, the initial kinetic energy is:
Kinetic Energy (initial) = (1/2) * 0.05 kg * (25 m/s)^2
= 0.5 * 0.05 kg * 625 m^2/s^2
= 15.625 J
Now, the car's speed triples to 75 m/s. Plugging this into the equation, the final kinetic energy is:
Kinetic Energy (final) = (1/2) * 0.05 kg * (75 m/s)^2
= 0.5 * 0.05 kg * 5625 m^2/s^2
= 140.625 J
To find the ratio of the final kinetic energy to the initial kinetic energy, we divide the final kinetic energy by the initial kinetic energy:
Ratio = Kinetic Energy (final) / Kinetic Energy (initial)
= 140.625 J / 15.625 J
= 9
Therefore, the kinetic energy of the blue car increases by a factor of 9 or 9 times.