To keep a lorry moving at a constant speed v, requires power p, from the engine. The force provided by the engine is

Analyze the question: A lorry moves at constant speed v, and the engine supplies power p. We need the force the engine provides.

Concept: Power is the rate of doing work:

P = Work done / time = (F × d) / t

Since d/t = v (speed), this gives:

P = F × v

Solution:

Using P = Fv, with power p and speed v:

p = F × v

Dividing both sides by v:

F = p / v

Checking the options:

• A. ½v is not dimensionally a force. Wrong.
• B. pv has units of W·m/s, which is not N. Wrong.
• C. p/v has units of W/(m/s) = (N·m/s)/(m/s) = N. Correct.
• D. pv² is wrong dimensionally.
• E. p/v² is wrong dimensionally.

Exam tip: Remember the triangle P = F × v. If you need F, divide power by velocity. When stuck, check units. Force must come out in newtons, and only p/v does that. Also, because the speed is constant, the engine force equals the resistive forces (friction and air resistance), so there is no net force.