The area under a force-time graph represents--------

Step 1: Analyze the question We are asked what quantity is represented by the area under a force-time (F-t) graph.

Step 2: Explain the concept The area under any graph is found by multiplying the quantities on the two axes (for a constant value, or by integration when it varies).

• Y-axis: Force (F), in newtons (N)
• X-axis: Time (t), in seconds (s)

So the area = F × t, which is called impulse.

From Newton's second law:

F = ma = m(v − u)/t

Multiplying both sides by t:

F × t = m(v − u) = mv − mu

So Impulse = Ft = change in momentum.

Step 3: Check the other options

• A. Change in kinetic energy: this comes from the area under a force-distance graph (work done), not force-time.
• C. Change in work done: work = force × distance, so it comes from a force-distance graph.
• D. Change in internal energy: this is related to heat and work in thermodynamics, not to a force-time graph.

Step 4: Answer The area under a force-time graph is the impulse, which equals the change in momentum.

Tip: Remember the pairs:

• Force-time graph → area = impulse (change in momentum)
• Force-distance graph → area = work done (energy)

Check the x-axis first, and you will know the answer straight away.