Question

A car moves at a speed of $20~ms^{-1}$ under a force of 500 N. The power output of the car is ________.

• A. 9.8 kW
• B. 980 kW
• C. 98 kW
• D. 10 kW
• E. 100 kW

Hint:

Power = Force $\times$ Velocity.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
Power is the rate at which work is done or energy is transferred. When an object is moving at a constant velocity under the action of a constant force, the power delivered by that force is the product of the force and the velocity.
Step 2: Key Formula or Approach
The formula for power (\(P\)) delivered by a constant force (\(F\)) acting on an object moving with a constant velocity (\(v\)) in the direction of the force is:
\[ P = F \cdot v \] The units will be Watts (W), where 1 W = 1 N \(\cdot\) m/s. The question asks for the answer in kilowatts (kW), where 1 kW = 1000 W.
Step 3: Detailed Explanation
1. List the given values.
- Force, \(F = 500 \text{ N}\)
- Speed (velocity), \(v = 20 \text{ ms}^{-1}\)
2. Calculate the power in Watts.
\[ P = F \times v \] \[ P = 500 \text{ N} \times 20 \text{ ms}^{-1} \] \[ P = 10000 \text{ W} \] 3. Convert the power to kilowatts.
To convert from Watts to kilowatts, we divide by 1000.
\[ P = \frac{10000}{1000} \text{ kW} \] \[ P = 10 \text{ kW} \] Step 4: Final Answer
The power output of the car is 10 kW.