1.

A particle of mass m is at rest at the origin at time t = 0.It is subjected to a force F(t)=F_(0)e^(-bt) in the x direction. Its speed v(t) is depicted by which of the following curves ?

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Solution :`F=ma=F_(0)e^(-BT)`
`(dv)/(dt)=(F_(0))/(m)e^(-bt)`
`underset(0)overset(v)INT dv=(F_(0))/(m)underset(0)overset(t)int e^(-bt)dt=(F_(0))/(m)((e^(-bt))/(-B))_(0)^(t)`
`v=(F_(0))/(mb)(1-e^(-bt))`
So, CORRECT choice is (d).


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