A particle moving along the x-axis has acceleration f at time t given by f = 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 f = 0, the particle's velocity vₓ is:
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Question

A particle moving along the x-axis has acceleration f at time t given by f = 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 f = 0, the particle's velocity vₓ is:

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G1 Physics · Accepted Answer

Step 1: f becomes zero at t=T. Step 2: Since dv/dt=f₀(1−t/T), integrate from 0 to T: v = ∫₀ᵀ f₀(1−t/T)dt. Step 3: v = f₀[T−T/2] = ½f₀T. Final answer: C.

A particle moving along the x-axis has acceleration f at time t given by f = 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 f = 0, the particle's velocity vₓ is: