Question

Area under velocity-time graph gives

• A. displacement
• B. work
• C. acceleration
• D. moment

Hint:

In kinematics, the area under the velocity-time graph represents displacement, while the area under a force-distance graph represents work.

Answer 1

The Correct Option is A

Step 1: Understand the meaning of area under a velocity-time graph.
In a velocity-time graph, the area under the graph represents the displacement. This is because displacement is the integral of velocity over time.
Step 2: Conclusion.
Thus, the area under the velocity-time graph gives the displacement, corresponding to option (A).

Answer 2

This question can be answered by checking the physical units involved. On a velocity-time graph, the vertical axis is velocity (m/s) and the horizontal axis is time (s). The area under the graph is the product of these two axes' quantities. Let's check what each option's unit would require, and compare it against what this product actually gives.

1. Displacement: Multiplying velocity (m/s) by time (s) gives units of meters (m), which is exactly the unit of displacement. This matches.
2. Work: Work is measured in joules (kg·m²/s²), which requires a force term, not just velocity and time. The area under a velocity-time graph has no force or mass component, so it cannot represent work.
3. Acceleration: Acceleration has units of m/s², which comes from dividing velocity by time (the graph's slope), not multiplying them (the graph's area). So this does not match the area calculation.
4. Moment: Moment (or torque) is measured in newton-meters (kg·m²/s²), again requiring a force component that is absent from a plot of velocity against time.

Only the displacement option has units consistent with velocity multiplied by time.

Therefore, the correct answer is displacement.