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A particle moves with velocity given by v = v0 + gt + ft². If its position is x = 0 at t = 0, what is its displacement at t = 1?

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

Correct answer: v0 + g/2 + f/3

Solution

x = integral_0^1 (v0 + g*t + f*t^2) dt = v0 + g/2 + f/3. The t^2 term integrates to f/3, not f/2.

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