A particle moving along X-axis has acceleration f,
at time t, given f =
where f, and T are
wconstants. The particle at t = 0 has zero velocity.
When f = 0, the particle's velocity (Vx) is
[AIPMT (Prelims)-2007]
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Instantaneous velocity at the instant when t = 0, a = ao(1 - t/T), When a = 0, t = T, a = ao(1 - t/T), dv/dt = ao(1 - t/T), dv = ao(1 - t/T) dt,
Integrate, v = ao(t - t²/(2T)), When t = T (i.e when a = 0), v = ao(T - T²/(2T)), v = ao(T/2). Therefore, velocity at the instant when a = 0 is = ao(T/2)
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Answer:
Instantaneous velocity
t = 0
a not ( 1 - t/T)
if a = 0
t = t
dv/dt = a not ( 1 - t/T)
Instantaneous velocity at the instant when t = 0, a = ao(1 - t/T), When a = 0, t = T, a = ao(1 - t/T), dv/dt = ao(1 - t/T), dv = ao(1 - t/T) dt,
Integrate, v = ao(t - t²/(2T)), When t = T (i.e when a = 0), v = ao(T - T²/(2T)), v = ao(T/2). Therefore, velocity at the instant when a = 0 is = ao(T/2)
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