With brakes fully applied, a 1340 kg car deccelerates from a speed of 96.0 km/hr. What is the change in the kinetic energy of the car?
To find the change in kinetic energy of the car, we need to calculate the initial kinetic energy and the final kinetic energy, and then calculate the difference between them.
The formula for kinetic energy is:
Kinetic Energy = 1/2 * mass * velocity^2
First, let's convert the speed from kilometers per hour (km/hr) to meters per second (m/s) since the formula requires the velocity in meters per second.
To convert from km/hr to m/s, we divide the speed by 3.6, since there are 3.6 seconds in an hour.
Given:
Mass of the car (m) = 1340 kg
Initial velocity (Vi) = 96.0 km/hr
Step 1: Convert Initial Velocity (Vi) to meters per second (m/s)
Vi = 96.0 km/hr
Vi = 96.0 * (1000 m/1 km) / (3600 s/1 hr) [Converting km/hr to m/s]
Vi = 26.67 m/s
Step 2: Calculate the initial kinetic energy (Ki)
Ki = 1/2 * m * Vi^2
Ki = 1/2 * 1340 kg * (26.67 m/s)^2
Ki = 1/2 * 1340 kg * 711.289 m^2/s^2
Ki = 238,826.06 J
Now, we need to calculate the final kinetic energy (Kf) when the car comes to a complete stop.
Given:
Final velocity (Vf) = 0 m/s (since the car comes to a stop)
Step 3: Calculate the final kinetic energy (Kf)
Kf = 1/2 * m * Vf^2
Kf = 1/2 * 1340 kg * (0 m/s)^2
Kf = 0 J
Step 4: Calculate the change in kinetic energy (ΔK)
ΔK = Kf - Ki
ΔK = 0 J - 238,826.06 J
ΔK = -238,826.06 J
The change in kinetic energy (ΔK) of the car is -238,826.06 Joules. Note that the negative sign indicates a decrease in kinetic energy, as the car is decelerating and coming to a stop.