Question

An electron moving along the x axis has a position given by x 16te$t m, where t is in seconds. How far is the electron from the origin when it momentarily stops

Answer 1

This question is incomplete, the complete question is;

An electron moving along the x axis has a position given by x = 16 t$e^{-t}$ m, where t is in seconds. How far is the electron from the origin when it momentarily stops

Answer:

the electron is 5.88 m far from the origin when it momentarily stops

Explanation:

Given that;

the position of the electron is x =  16 t$e^{-t}$ m

now, if the electron stopped after a time t, then its velocity is zero

so

V = dx/dt = 0

d/dt( 16 t$e^{-t}$ m) = 0

16( -t$e^{-t}$ + $e^{-t}$ ) = 0

16(-t + 1) $e^{-t}$ = 0

16(1 - t) $e^{-t}$ = 0

1 - t = 0

t = 1 sec

so

x = 16 × 1 × $e^{-1}$ m

x = 16 × 1 × 0.36787 m

x = 5.88 m

Therefore, the electron is 5.88 m far from the origin when it momentarily stops