A particle executes the motion described by x(f) =x_(0) (1- e ^(lamda t) ) , t ge 0, x_(0) gt 0. (a) Where does the particle start and with what velocity ? (b) Find maximum and minimum values of x(t), v(t), a(t). Show that X(t) and alt) increase with time and v(t) decreases with time.

A particle executes the motion described by x(f) =x_(0) (1- e ^(lamda

1.	A particle executes the motion described by x(f) =x_(0) (1- e ^(lamda t) ) , t ge 0, x_(0) gt 0. (a) Where does the particle start and with what velocity ? (b) Find maximum and minimum values of x(t), v(t), a(t). Show that X(t) and alt) increase with time and v(t) decreases with time.
Answer» SOLUTION :Given, `x (t) = x _(0) (1- e ^( - gammat ))` `v (t) = (dx(t))/( dt ) = x _(0) gamma e ^(- gammat )` `a (t) = (DV(t))/(dt) =- x _(0) gamma ^(2) e ^(- gamma t)` (a) When `t =0, x (t) = x _(0) (1- e ^(-0)) =x_(0) (1-1) =0` `v (t) = x _(0) gamma e ^(-0) = x _(0) gamma (1) = gamma x _(0)` (b) `x (t)` is maximum when `t = oo` `[x (t) ] _(max) = x _(0) (1-0) = x _(0)` `x(t)` is minimum when `t =0` `[x (t) ]_(min) =0` v(t) is maximum when `t =0, v (0) = x _(0) gamma` v (t) is maximum when `t = oo, v (oo) =0` ` a (t)` is maximum when `t =oo, a (oo) =0` a (t) is minimum when `t =0, a (0) =- x_(0) gamma ^(2)` Note: We should he careful about NATURE of variation of the curve and maximum and minimum value will be DECIDED accordingly.