This question is incomplete, the complete question is;
An electron moving along the x axis has a position given by x = 16 t[tex]e^{-t}[/tex] 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[tex]e^{-t}[/tex] m
now, if the electron stopped after a time t, then its velocity is zero
so
V = dx/dt = 0
d/dt( 16 t[tex]e^{-t}[/tex] m) = 0
16( -t[tex]e^{-t}[/tex] + [tex]e^{-t}[/tex] ) = 0
16(-t + 1) [tex]e^{-t}[/tex] = 0
16(1 - t) [tex]e^{-t}[/tex] = 0
1 - t = 0
t = 1 sec
so
x = 16 × 1 × [tex]e^{-1}[/tex] 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
