A Car Speeds Up While the Engine Delivers Constant Power
Introduction
When a car speeds up, the engine must deliver more power to overcome the increased drag and resistance. However, if the engine is delivering constant power, the car’s acceleration will decrease as its speed increases.
The Relationship Between Power, Force, and Acceleration
The power delivered by an engine is equal to the force applied to the car multiplied by the car’s velocity. In other words:
$$P = Fv$$
where:
* $$P$$ is power in watts
* $$F$$ is force in newtons
* $$v$$ is velocity in meters per second
The acceleration of a car is equal to the force applied to the car divided by the car’s mass. In other words:
$$a = F/m$$
where:
* $$a$$ is acceleration in meters per second squared
* $$F$$ is force in newtons
* $$m$$ is mass in kilograms
Constant Power and Decreasing Acceleration
If the engine is delivering constant power, then the force applied to the car will decrease as the car’s speed increases. This is because the power delivered by the engine is equal to the force applied to the car multiplied by the car’s velocity. As the car’s speed increases, the force applied to the car must decrease in order to keep the power constant.
The decreasing force applied to the car will result in a decreasing acceleration. This is because the acceleration of a car is equal to the force applied to the car divided by the car’s mass. As the force applied to the car decreases, the acceleration will also decrease.
Example
Consider a car with a mass of 1000 kg and an engine that delivers a constant power of 100 kW. The car is initially at rest.
When the car starts to move, the engine will apply a force to the car. This force will cause the car to accelerate. As the car’s speed increases, the force applied to the car will decrease in order to keep the power constant.
The following table shows the relationship between the car’s speed, the force applied to the car, and the car’s acceleration:
| Speed (m/s) | Force (N) | Acceleration (m/s^2) |
|—|—|—|
| 0 | 10000 | 10 |
| 10 | 9091 | 9.09 |
| 20 | 8333 | 8.33 |
| 30 | 7692 | 7.69 |
| 40 | 7143 | 7.14 |
| 50 | 6667 | 6.67 |
As you can see from the table, the force applied to the car decreases as the car’s speed increases. This results in a decreasing acceleration.
Conclusion
When a car speeds up, the engine must deliver more power to overcome the increased drag and resistance. However, if the engine is delivering constant power, the car’s acceleration will decrease as its speed increases.
