The kinetic energy of an object is given by the equation:
KE = 0.5 * mass * velocity^2
To understand why the kinetic energy of a car traveling at 10 m/s is four times that of a car traveling at 5 m/s, we can compare the two scenarios.
Let's assume that the masses of the two cars are the same for simplicity. In that case, the kinetic energy equation can be simplified to:
KE1 = 0.5 * m * v1^2 (for the car traveling at 5 m/s) KE2 = 0.5 * m * v2^2 (for the car traveling at 10 m/s)
We can calculate the ratio of the kinetic energies:
KE2 / KE1 = (0.5 * m * v2^2) / (0.5 * m * v1^2)
The mass of the cars (m) is common to both equations, so it cancels out:
KE2 / KE1 = (v2^2) / (v1^2)
Now, let's substitute the given velocities:
KE2 / KE1 = (10^2) / (5^2) = 100 / 25 = 4
Therefore, the kinetic energy of the car traveling at 10 m/s is four times the kinetic energy of the car traveling at 5 m/s. This is because the kinetic energy is directly proportional to the square of the velocity. When the velocity doubles (from 5 m/s to 10 m/s), the kinetic energy increases by a factor of four.