Source: Extra Practice
The velocity of a particle moving along the x-axis is given by v(t) = 3t² + 2t m/s. Find the displacement of the particle from t = 0 to t = 2 seconds.
Options
Option A
10 m
Option B is correct
12 m
Option C
14 m
Option D
16 m
Explanation
Displacement is calculated by the definite integral of velocity with respect to time: s = ∫₀² (3t² + 2t) dt. First, find the antiderivative: ∫ (3t² + 2t) dt = t³ + t². Now, apply the limits from 0 to 2: [t³ + t²] evaluated from 0 to 2 = (2³ + 2²) - (0³ + 0²) = (8 + 4) - 0 = 12 meters. Option 1 (10 m) is a common calculation error where one term is missed. Options 3 and 4 are incorrect numerical results arising from improper application of the upper limit.