A particle moving along x-axis has acceleration f, at time t, given by f = f0 (1-t/T), where f0 and T are constants…

Q: A particle moving along x-axis has acceleration f, at time t, given by $ f = f_0 (1-\frac{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

(a) f0T

(b) (1/2) f0T2

(c) f0T2

(d) (1/2) f0T

Ans: (d)
Sol: Putting f = 0

$ \displaystyle f_0(1-\frac{t}{T}) = 0 $

Hence , t = T

$ \displaystyle \int_{0}^{v}dv = \int_{0}^{T}f dt $

$ \displaystyle v = \int_{0}^{T}f_0(1-\frac{t}{T}) dt $