The velocity-time relation of a particle is v = 6 - 2t m s⁻¹ for 0 ≤ t ≤ 3 s. Find its displacement in this interval using area under the v-t curve.
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The velocity-time relation of a particle is v = 6 − 2t m s⁻¹ for 0 ≤ t ≤ 3 s. Find its displacement in this interval using area under the v-t curve.

G1 Physics · Accepted Answer

Displacement equals the signed area under the velocity-time curve. Here v remains non-negative from t=0 to3. Displacement = ∫₀³(6−2t)dt = [6t−t²]₀³ = 18−9 = 9 m.