A particle moving along x-axis has acceleration aₓ at time t, given by aₓ = f₀ (1 − t/T), where f₀ and T are constants. The particle at t = 0 has zero velocity. In the time interval between t = 0 and the instant when t = T, the particle’s velocity (vₓ) is:

Question

Accepted Answer

1/2 f₀T. The velocity is obtained by integrating acceleration with respect to time. Integrating aₓ = f₀(1 − t/T) from t = 0 to t = T gives vₓ = ∫[0 to T] f₀(1 − t/T) dt = f₀[T − (T²/2T)] = (1/2)f₀T. Hence, the correct answer is C.

A particle moving along x-axis has acceleration aₓ at time t, given by aₓ = f₀ (1 − t/T), where f₀ and T are constants. The particle at t = 0 has zero velocity. In the time interval between t = 0 and the instant when t = T, the particle’s velocity (vₓ) is:

Solution

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