Question

The Area under velocity-time graph is :

• A. Displacement
• B. Velocity
• C. Acceleration
• D. Force

Answer 1

Answer:

A. Displacement

Velocity-Time Graph Mechanics

• The area enclosed between the velocity-time (v-t) graph and the time axis is numerically equal to the displacement (or total distance, if velocity is strictly positive) covered by the object during a specific time interval.

• Mathematical Basis: The unit of the area can be derived as: (Velocity units) × (Time units) = (m/s) × (s) = meters (m). Since the unit of displacement is meters, the area represents displacement.

• Graph Interpretation:

  • If the object moves with uniform velocity, the graph is a straight line parallel to the time axis. The area under this graph forms a rectangle, where Area = velocity × time.

  • If the object moves with uniform acceleration starting from rest, the graph is a straight line passing through the origin. The area forms a triangle, where Area = 0.5 × base × height.

  • For non-uniform motion, the area is calculated using integration: s = ∫v dt.

• Slope of v-t graph represents acceleration.

  • Area under v-t graph represents displacement.

  • Slope of position-time (x-t) graph represents velocity.