A car of mass 1,700 kg is initially traveling at a speed of 25 m/s. The driver then accelerates to a speed of 35 m/s over a distance of 500 m. Calculate the change in the kinetic energy of the car.
The initial speed is V1 = 25 m/s
The final speed is V2 = 35 m/s
The mass M = 1700 kg does not change.
Compute (M/2)(V2^2 - V1^2)
The distance over which the acceleration happens does not affect the answer.
To calculate the change in kinetic energy of the car, we need to find the initial kinetic energy and the final kinetic energy, and then subtract the initial from the final.
The formula for kinetic energy is:
Kinetic Energy (KE) = 1/2 * mass * velocity^2
First, let's calculate the initial kinetic energy:
Mass (m) = 1,700 kg
Initial Velocity (v1) = 25 m/s
Initial Kinetic Energy (KE1) = 1/2 * m * v1^2
= 1/2 * 1,700 kg * (25 m/s)^2
= 1/2 * 1,700 kg * 625 m^2/s^2
= 525,625 J
Next, let's calculate the final kinetic energy:
Final Velocity (v2) = 35 m/s
Final Kinetic Energy (KE2) = 1/2 * m * v2^2
= 1/2 * 1,700 kg * (35 m/s)^2
= 1/2 * 1,700 kg * 1,225 m^2/s^2
= 1,042,750 J
Now, we can find the change in kinetic energy by subtracting the initial kinetic energy from the final kinetic energy:
Change in Kinetic Energy = KE2 - KE1
= 1,042,750 J - 525,625 J
= 517,125 J
Therefore, the change in kinetic energy of the car is 517,125 Joules (J).