A particle moving along the x-axis has a pasition given by ` x= 10 t e^(-1)` metres where (t) is in seconds . How for is the partile from the origin when it momentarily stops ? (Do no consider its stop at infinity ).

Explanation

` x=10 t e^(-1)`
Instantaneus veocity,
` v= (dx) /(dt) =10 t (-1)e^(-t) + 10 e^(-t)`
`=e^(-t) (10 -10 t)`
Foe the body to be at rest, ` v=0`
S0, ` e^(-t) (10- 10 t) =0`
:. T= prop or 1 s`
But ` t= prop is not allowed , so ` t= 1s`
Thus ` x =1= xx 1 xx e^(-t) = (10//e) ` metres.