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Velocity–time graphs

Free notes · JEE Main Physics

Formulas

Δx=∫v dt=area under v–t\Delta x = \int v\, dt = \text{area under } v\text{–}t

Displacement as the v–t area

Worked example

A body's v–t graph is a triangle: 0 to 10 m/s in 5 s, then back to 0 in 5 s. Find the total distance.

  1. Distance = area under the v–t curve.
  2. First triangle: ½ × 5 × 10 = 25 m; second triangle: ½ × 5 × 10 = 25 m.
  3. Total = 50 m.

Answer: 50 m.