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Find the velocity of a particle at time t = T if its initial velocity is f0 and its acceleration is given by dv/dt = f0(1 - t/T).

1. f = f0(1 - t/T)
2. dv/dt = f0(1 - t/T)
3. v_x = ∫ dv = ∫ f0(1 - t/T) dt
4. v_x = f0T(1 - t/T)

Correct answer: v_x = f0T(1 - t/T)

Solution

The acceleration is given as dv/dt = f0(1 - t/T). Integrating this with respect to time gives v = ∫f0(1 - t/T) dt = f0T(1 - t/T) + C. Using the initial condition v = f0 at t = 0, we find C = f0T. Thus, the velocity at time t = T is v_x = f0T(1 - t/T).

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