The total area under a force-velocity graph represents

Analyze the question: We have a graph with force (F) on the vertical axis and velocity (v) on the horizontal axis. The area under a graph is the product of the two quantities, integrated over the horizontal axis. So we need to work out what F × v represents.

Concept: The area under a graph of y against x is ∫y dx. Here that means ∫F dv. For a constant force, this is simply F × v.

Solution:

• Power = Work done ÷ time = (F × d) ÷ t
• Since d ÷ t = v, we get Power = F × v

So the product of force and velocity has the units:

• N × m/s = J/s = Watt, the unit of power.

Checking the other options:

• Energy (A): Energy = force × distance, which would need a force-distance graph.
• Momentum (B): Momentum = mass × velocity. A force-time graph gives impulse (change in momentum), not a force-velocity graph.
• Pressure (D): Pressure = force ÷ area, which does not come from F × v.

Answer: The area under a force-velocity graph has units of N·m/s, which is power.

Tip: To identify what the area under a graph means, multiply the units of the two axes.

• Force × distance → energy (J)
• Force × time → impulse (N·s)
• Force × velocity → power (W)