A particle moves along x-axis with acceleration `a = a0 (1 – t// T)` where `a_(0)` and T are constants if velocity at t = 0 is zero then find the average velocity from t = 0 to the time when a = 0.

Answer

`a_(0)T//3`

Explanation

`a=a_(0)(1-t/T)` where `a_(0)` & `T` are constant
`underset(0)overset(v)(int)dv=a_(0)underset(t=0)overset(t)(int)(1-1/T)dt rArr v=a_(0)[t-t^(2)/(2T)]`
`rArr int dx=a_(0) underset(t=0)overset(t)(int)[t-t^(2)/(2T)]dt`
For `a=0rArr 1-t/T=0" "t=T" "a_(0)[t^(2)/2-t^(3)/(6T)]`
`:. lt v gt =(underset(0)overset(T)(int)v dt)/(underset(0)overset(T)(int)dt)=(a_(0)[T^(2)/2-T^(3)/(6T)])/T=(a_(0)T)/3`