A 1000 Kg sports car accelerates from 0 to 30m/s in 10 s. What is the average power of the engine?
A 1000 Kg sports car accelerates from 0 to 30m/s in 10 s. What is the average power of the engine?
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![**Problem 7: Calculating Average Power of an Engine**
A 1000 kg sports car accelerates from 0 to 30 m/s in 10 seconds. What is the average power of the engine?
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To solve this problem, consider applying the principles of physics related to acceleration, work, and power.
**Steps to Solve:**
1. **Calculate the acceleration (a):**
Use the formula:
\[ a = \frac{{v_f - v_i}}{t} \]
where \( v_f = 30 \text{ m/s} \), \( v_i = 0 \text{ m/s} \), and \( t = 10 \text{ s} \).
2. **Determine the work done (W):**
The work done on the car is equal to the change in kinetic energy:
\[ W = \Delta KE = \frac{1}{2} m v_f^2 - \frac{1}{2} m v_i^2 \]
where \( m = 1000 \text{ kg} \).
3. **Calculate the average power (P):**
Power is the work done per unit time, calculated with:
\[ P = \frac{W}{t} \]
By following these steps, you can determine the average power output of the engine over the 10-second interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F659ca555-9d28-4154-b7a3-72a82930f29f%2Fcb6d51b0-87ae-49f7-b5df-61286cfbb98d%2Fsnqc3ga_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 7: Calculating Average Power of an Engine**
A 1000 kg sports car accelerates from 0 to 30 m/s in 10 seconds. What is the average power of the engine?
---
To solve this problem, consider applying the principles of physics related to acceleration, work, and power.
**Steps to Solve:**
1. **Calculate the acceleration (a):**
Use the formula:
\[ a = \frac{{v_f - v_i}}{t} \]
where \( v_f = 30 \text{ m/s} \), \( v_i = 0 \text{ m/s} \), and \( t = 10 \text{ s} \).
2. **Determine the work done (W):**
The work done on the car is equal to the change in kinetic energy:
\[ W = \Delta KE = \frac{1}{2} m v_f^2 - \frac{1}{2} m v_i^2 \]
where \( m = 1000 \text{ kg} \).
3. **Calculate the average power (P):**
Power is the work done per unit time, calculated with:
\[ P = \frac{W}{t} \]
By following these steps, you can determine the average power output of the engine over the 10-second interval.
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