To accelerate your car at a constant acceleration, the car’s engine must
A) maintain a constant turning speed.
C) develop ever-decreasing power.
B) maintain a constant power output.
D) develop ever-increasing power.
The correct answer and explanation is:
The correct answer is D) develop ever-increasing power.
To understand why, we need to consider the relationship between power, force, and acceleration. Power is the rate at which work is done or energy is transferred. In the case of a car accelerating at a constant rate, the engine must provide power to overcome the car’s inertia and increase its speed.
At a constant acceleration, the car’s velocity is increasing over time. Since power is the product of force and velocity (P = F × v), for the car to maintain a constant acceleration, the force the engine produces must not remain constant. As the car speeds up, its velocity increases, and to continue accelerating at the same rate, the engine must generate more power.
When the car is moving faster, it takes more energy to keep increasing its speed because the resistance from friction, air drag, and other factors increases with velocity. The engine must counter these forces and still produce enough work to keep the car accelerating at the same rate. Therefore, the power output of the engine needs to increase as the car accelerates.
This is why a car’s engine develops ever-increasing power during constant acceleration. If the engine were to maintain a constant power output, the acceleration would decrease as the car’s velocity increases. Similarly, if the engine were to maintain a constant turning speed or develop decreasing power, the car would not be able to accelerate at a steady rate.