The driver of a 1300-kg car moving at 21 m/s brakes quickly to 13 m/s when he spots a local garage sale.
(a) Find the change in the car's kinetic energy.
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To find the change in the car's kinetic energy, we need to calculate the initial kinetic energy (KEi) and the final kinetic energy (KEf), and then subtract the initial value from the final value.
The formula for kinetic energy is:
KE = 0.5 * m * v^2
Where:
KE is the kinetic energy,
m is the mass of the car, and
v is the velocity/speed of the car.
Step 1: Calculate the initial kinetic energy (KEi):
KEi = 0.5 * m * v^2
Given:
m = 1300 kg
v = 21 m/s
Plugging the values into the equation, we get:
KEi = 0.5 * 1300 kg * (21 m/s)^2
Simplifying the equation, we have:
KEi = 0.5 * 1300 kg * 441 m^2/s^2
KEi = 0.5 * 573300 kg m^2/s^2
KEi = 286650 kg m^2/s^2
Step 2: Calculate the final kinetic energy (KEf):
KEf = 0.5 * m * v^2
Given:
v = 13 m/s
Plugging the values into the equation, we get:
KEf = 0.5 * 1300 kg * (13 m/s)^2
Simplifying the equation, we have:
KEf = 0.5 * 1300 kg * 169 m^2/s^2
KEf = 0.5 * 219700 kg m^2/s^2
KEf = 109850 kg m^2/s^2
Step 3: Calculate the change in kinetic energy (ΔKE):
ΔKE = KEf - KEi
Plugging in the values, we get:
ΔKE = 109850 kg m^2/s^2 - 286650 kg m^2/s^2
ΔKE = -176800 kg m^2/s^2
Therefore, the change in the car's kinetic energy is -176800 kg m^2/s^2.