A car of mass 1900kgs accelerates from rest to a speed of 27ms-1 in 8.1s.Calculate the average rate at which kinetic energy is supplied to the car during the acceleration.
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To calculate the average rate at which kinetic energy is supplied to the car during the acceleration, we can use the formula:
Average Power = Change in kinetic energy / Time taken
First, let's calculate the change in kinetic energy:
Initial kinetic energy = 0 (since the car starts from rest)
Final kinetic energy = 0.5 * mass * (final velocity)^2
Final velocity = 27 m/s
Mass = 1900 kg
Final kinetic energy = 0.5 * 1900 * (27)^2
Now, let's calculate the time taken:
Time taken = 8.1 seconds
Now, substitute the values into the formula:
Average Power = (0.5 * 1900 * (27)^2) / 8.1
Calculating the average power, we get:
Average Power = 51054.32 Watts
Therefore, the average rate at which kinetic energy is supplied to the car during the acceleration is approximately 51054.32 Watts.
To calculate the average rate at which kinetic energy is supplied to the car, we need to find the change in kinetic energy and divide it by the time taken.
The formula for kinetic energy is given by:
Kinetic energy (KE) = (1/2) * mass * velocity^2
First, let's find the initial kinetic energy (KE_initial) when the car is at rest. Since the car is at rest, its velocity is 0, so KE_initial = (1/2) * mass * 0^2 = 0.
Next, we need to find the final kinetic energy (KE_final) when the car reaches a speed of 27 m/s. Using the formula, we have:
KE_final = (1/2) * mass * velocity^2
= (1/2) * 1900 kg * (27 m/s)^2
= 689,265 J (joules)
The change in kinetic energy (ΔKE) is given by the difference between the final and initial kinetic energies:
ΔKE = KE_final - KE_initial
= 689,265 J - 0 J
= 689,265 J
Now, we can calculate the average rate at which kinetic energy is supplied to the car by dividing the change in kinetic energy by the time taken:
Average rate = ΔKE / time
= 689,265 J / 8.1 s
≈ 85,030 J/s
Therefore, the average rate at which kinetic energy is supplied to the car during the acceleration is approximately 85,030 J/s.