An electric vehicle is driven by a motor which produces a constant driving force - AQA - A-Level Physics - Question 17 - 2019 - Paper 1

To determine the variation of power over time, we need to consider the relationship between force, velocity, and power. The power developed by the motor can be expressed as:

$P = F imes v$

Where:

• $P$ is the power,
• $F$ is the force (constant driving force), and
• $v$ is the velocity of the vehicle.

As the vehicle starts from rest and accelerates due to the constant force, the velocity $v$ increases over time. Therefore, as time progresses, the power $P$ will also increase since it is directly proportional to the velocity. This indicates that the power does not remain constant; rather, it increases from zero as the vehicle gains speed.

• Option A is incorrect because power cannot stay constant as the vehicle accelerates.
• Option B states that it increases linearly from zero, which is not accurate since the relationship is quadratic due to the increasing velocity over time.
• Option C is correct as it reflects the non-linear increase in power due to the dependence on the square of velocity during acceleration.
• Option D is incorrect because the power will not decrease after reaching a maximum; it continues to increase as long as the vehicle accelerates.

Thus, the best choice is C: It increases non-linearly from zero.