To find the work done on the car and the power delivered by the engine during its acceleration, we can break the problem down into manageable steps. Let's tackle each part systematically.
Calculating Work Done on the Car
The work done on an object can be calculated using the formula:
Work (W) = Change in Kinetic Energy (ΔKE)
The kinetic energy of an object is given by:
KE = 0.5 * m * v²
Where:
- m is the mass of the object (in kg)
- v is the final velocity (in m/s)
In this case, the car starts from rest, so its initial velocity (u) is 0 m/s. The final velocity (v) is 14.7 m/s, and the mass (m) of the car is 1.04 x 10³ kg.
First, we calculate the final kinetic energy:
KE_final = 0.5 * (1.04 x 10³ kg) * (14.7 m/s)²
Calculating this gives:
KE_final = 0.5 * 1040 * 216.09 = 112896.3 J
Since the initial kinetic energy (KE_initial) is 0 (the car starts from rest), the change in kinetic energy is:
ΔKE = KE_final - KE_initial = 112896.3 J - 0 = 112896.3 J
Thus, the work done on the car is:
W = 112896.3 J
Determining Power Delivered by the Engine
Power is defined as the rate at which work is done. The formula for power (P) is:
P = Work / Time
From our previous calculation, we found that the work done on the car is 112896.3 J. The time interval during which this work is done is 3.82 seconds.
Now, we can calculate the power:
P = 112896.3 J / 3.82 s
Calculating this gives:
P ≈ 29505.4 W
To convert this into kilowatts (kW), we divide by 1000:
P ≈ 29.5 kW
Summary of Results
In summary, the work done on the car during its acceleration is approximately 112896.3 J, and the power delivered by the engine during this time interval is about 29.5 kW.
