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A particle executes the motion described...

A particle executes the motion described by
`x(t)=x_(0)(1-e^(-gammat)),tge0,x_(0)>0`.
The maximum and minimum values of `v(t)` are

Text Solution

Verified by Experts

Give x(t)=`x_(0)(1-e^(-1))`
`v=(dx)/(dt)=x_(0)e^(-gammat)`
`a=(dv)/(dt)=-x_(0)^(2)e^(-t)`
(a) At `t=0,x=x_(0)(1-e^(-0))=x_(0)(1-1)=0`
and `v=x_(0)e^(-0)=x_(0)`
(b) x (t) is maximum, when t=`oo`, so x(t)=`x_(0)`
x(t) is minimum, when t=0, so `x(t)=0`
v(t) is maximum, when t=0, so `v(0)=gammax_(0)`
v(t) is minimum, when t=`oo`, so v(t)=0
a (t) is minimum, when t=`oo`, so a (t)=0
a (t) is maximum, when t=0, so a (0)=`-x_(0)gamma^(2)`
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