During an emergency stop, a 1.5x10^3-kilogram car lost a total of 3.0x10^5 joules of kinetic energy. What was the speed of the car at the moment the brakes were applied?
To find the initial speed of the car, we need to first find the final kinetic energy of the car at the moment the brakes were applied, and then use the equation for kinetic energy to find the initial speed.
Given:
Mass of the car, m = 1.5x10^3 kg
Loss of kinetic energy, ΔK = 3.0x10^5 J
The final kinetic energy of the car, after losing 3.0x10^5 J of kinetic energy, can be calculated using the formula:
Kf = Ki - ΔK
where Kf is the final kinetic energy and Ki is the initial kinetic energy.
Since the car comes to an emergency stop, we assume the final kinetic energy is zero (the car is not moving).
0 = Ki - 3.0x10^5 J
=> Ki = 3.0x10^5 J
Now we can use the equation for kinetic energy to find the initial speed of the car:
Ki = (1/2)mv^2
Rearranging the equation, we get:
v^2 = (2Ki) / m
Substituting the known values:
v^2 = (2 * 3.0x10^5 J) / (1.5x10^3 kg)
=> v^2 = 4.0x10^2 m^2/s^2
Taking the square root of both sides, we find:
v = √(4.0x10^2 m^2/s^2)
=> v = 2.0x10^1 m/s
=> v = 20 m/s
Therefore, the speed of the car at the moment the brakes were applied was 20 m/s.