An electric car of mass 1000kg uses twenty five 12v batteries connected together to create a p.d. of 300V. The car accelerates from rest to a speed of 30ms^-1 in 12 seconds. a) what is the final kinetic energy of the car? b) what is the power of the car? c) How much electrical current flows from the battery? What assumptions have you made in calculating a) to c)?

An electric car of mass 1000kg uses twenty five 12v batteries connected together to create a p.d. of 300V. The car accelerates from rest to a speed of 30ms^-1 in 12 seconds.

a) what is the final kinetic energy of the car?
b) what is the power of the car?
c) How much electrical current flows from the battery?
What assumptions have you made in calculating a) to c)?

Answer:

Explanation:

a) The final kinetic energy of the car is equal to the work done in accelerating the car from rest to a speed of 30ms^-1. Therefore, the final kinetic energy of the car is equal to:

KE = ½ mv^2 = ½(1000kg)(30ms^-1)^2 = 450,000 J

b) The power of the car can be calculated by dividing the work done by the time taken for the acceleration. Therefore, the power of the car is equal to:

Power = Work/Time = 450,000 J/12s = 37,500 W

c) The electrical current flowing from the battery can be calculated by dividing the power by the voltage of the battery. Therefore, the electrical current flowing from the battery is equal to:

Current = Power/Voltage = 37,500 W/300V = 125 A

Assumptions:

1. The car is assumed to be moving in a straight line with no friction.

2. The batteries are assumed to be wired correctly and in good condition.

3. The car is assumed to have a constant acceleration over the 12s period.

4. The voltage of the battery is assumed to remain constant over the 12s period.

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