Question

Particle imoves along the x-axis has acceleration f at time t

Answer 1

I'm answering its second part i.e instantaneous velocity at the instant when a = 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)