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.

A particle of mass m is at rest at the origin at time t=0. It is subje

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.
Answer» Solution :As the force is exponentially decreasing, its acceleration, i.e., rate of INCREASE of VELOCITY will decrease with time. Thus, the graph of velocity will be an increasing curve with decreasing SLOPE with time. `a=(F)/(m)=(F_(0))/(m)e^(-bt) RARR (dv)/(dt)=(F_(0))/(m)e^(-bt) rArr int_(0)^(v)dv=int_(0)^(t)(F_(0))/(m)e^(-bt)dt` `rArr v=[(F_(0))/(m)((1)/(-b))e^(-bt)]_(0)^(t)=[(F_(0))/(m)((1)/(b))e^(-bt)]_(t)^(0)` `=(F_(0))/(mb)(e^(0)-e^(-by))=(F_(0))/(mb)(1-e^(-bt))`