In an electric car, regenerative braking is used to recharge batteries.
The principle of regenerative braking involves converting the
kinetic energy of the vehicle into energy stored in a battery. If a
car is traveling at a speed of 30 km/h and is stopped completely
by braking, what would be the energy stored in the battery if the
mass of the car is 1000 kg and the energy conversion effi ciency is
assumed to be 100%? If this braking happens at a constant rate for
5 seconds, what is the average rate of power transfer?
To calculate the energy stored in the battery, we need to first calculate the kinetic energy of the car. The formula to calculate kinetic energy is:
Kinetic Energy (KE) = 0.5 * mass * velocity^2
Given:
Mass (m) = 1000 kg
Velocity (v) = 30 km/h = 8.33 m/s (converted from km/h to m/s)
Now we can calculate the kinetic energy:
KE = 0.5 * 1000 kg * (8.33 m/s)^2
= 0.5 * 1000 kg * 69.44 m^2/s^2
= 34,720 Joules
Since the energy conversion efficiency is assumed to be 100%, all the kinetic energy is converted and stored in the battery. Therefore, the energy stored in the battery would be 34,720 Joules.
Now let's calculate the average rate of power transfer during the 5-second braking period. The formula to calculate power is:
Power (P) = Energy (E) / time (t)
Given:
Energy (E) = 34,720 Joules
Time (t) = 5 seconds
Now we can calculate the average rate of power transfer:
P = 34,720 Joules / 5 seconds
= 6,944 Watts
Therefore, the average rate of power transfer during the 5-second braking period is 6,944 Watts.