Question

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 the particle at t= 0 has zero velocity. in the time interval between t =0 and the instant when f=0 the particles velocity is.....​

Answer 1

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Actually Welcome to the Concept of the Kinematics,

Now basically here, the Acceleration is given as f

such that Acceleration "f" depends on the function time as given,

f = f° ( 1-t /T)

thus now, since at, t= 0 , V = 0 ,

so at a instant we get as,

dv/dt = f

thus we get as,

integration of dv = integration of f. dt

from this we will get the concerned velocity.

thus we get here as,

dv = f°/T ( 1-t) dt

so after integration we get as

⭐V = f°/T ( 2t-t^2/2)