A particle is moving along x-axis with acceleration `a=a_(0)(1-t//T)` where `a_(0)` and T are constants. The particle at t=0 has zero velocity. Calcul

Question

A particle is moving along x-axis with acceleration `a=a_(0)(1-t//T)` where `a_(0)` and T are constants. The particle at t=0 has zero velocity. Calcul

A particle is moving along x-axis with acceleration `a=a_(0)(1-t//T)` where `a_(0)` and T are constants. The particle at t=0 has zero velocity. Calculate the average velocity between t=0 and the instant when a=0

Monjur Alahi

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2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

`a=(dv)/(dt)=a_(0)(1-(t)/(T))rArrint_(0)^(v)dv=int_(0)T(t)a_(0)(1-(t)/(T))dtrArrv=a_(0)(t-(t^(2))/(2T))`
`because (dx)/(dt)=v` so `intdx=intv dt rArr x=int_(0)^(t)a_(0)(t-(t^(2))/(2T))dtrArrx=a_(0)((t^(2))/(2)-(t^(3))/(6T))`
Now `a=0rArrt=T`
average velocity `=("displacement")/("time")=(a_(0)((T^(2))/(2)-(T^(3))/(6T)) )/(T)=(a_(0)T)/(3)`