An electron moving along the x-axis has a position given by x = Ate - Bt m, where t is in seconds and A and B are positive constants. In terms of A and B, how far is the electron from the origin...

An electron moving along the x-axis has a position given by x = Ate - Bt m, where t is in seconds and A and B are positive constants. In terms of A and B, how far is the electron from the origin when it momentarily stops?

nees101 | High School Teacher | (Level 2) Adjunct Educator

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Given that the position of an electron moving along the x-axis is given by `x=Ate^(-Bt)` , where A and B are constants.

Now we have to find how far is the electron from its origin before momentarily stopping.

If we know when it stops then we may be able to find where it is.

For that we find the instantaneous velocity and then equate it to zero.

Instantaneous velocity is given by:

v=dx/dt

= d/dt(Ate^(-Bt))

= A(-Bte^(-Bt)+e^(-Bt))

= Ae^(-Bt)(-Bt+1)

Now equating v=0 we get,

Ae^(-Bt)(-Bt+1)=0

i.e. -Bt+1=0

implies, t=1/B sec

So at t=1/B sec the electron stops and the position is given by:

x(1/B)=A(1/B)e^(-B(1/B))

= A/Be^(-1)  meters

i.e the electron stops momentarily at `x=A/B e^(-1) meters`