An advertisment claims that a certain 1200 kg car can accelerate from rest to a speed of 25 m/s in 8.0 s. what average power must the motor supply in order to cause this acceleration?
Kinetic energy change divded by 8 seconds is the average power.
Crank out the numbers
To calculate the average power required to cause this acceleration, we need to use the equation:
Power = Work / Time
In this case, the work done is equal to the change in kinetic energy. The change in kinetic energy is given by the equation:
Change in kinetic energy = 0.5 * mass * (final velocity^2 - initial velocity^2)
Given values:
Mass (m) = 1200 kg
Initial velocity (u) = 0 m/s
Final velocity (v) = 25 m/s
Time (t) = 8.0 s
First, let's calculate the change in kinetic energy:
Change in kinetic energy = 0.5 * 1200 kg * (25 m/s)^2 - 0.5 * 1200 kg * (0 m/s)^2
= 0.5 * 1200 kg * 625 m^2/s^2 = 375,000 J
Now, we can calculate the average power required:
Average power = Change in kinetic energy / Time
= 375,000 J / 8.0 s
= 46,875 W
Therefore, the motor must supply an average power of 46,875 Watts to cause this acceleration.