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The velocity of a particle is v = v₀ + gt + Ft². Its position is x = 0 at t = 0; then its displacement after time (t = 1) is:

1. v₀ + g + F
2. v₀ + g/2 + F/3
3. v₀ + g/2 + F
4. v₀ + 2g + 3F

Correct answer: v₀ + g/2 + F/3

Solution

x(1) = integral_0^1 (v0 + g t + F t^2) dt = v0 + g/2 + F/3.

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