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?
Position of the electron is x = Ate - Bt m (along the x-axis).
A and B are positive constants.
When the electron stops, its velocity is 0. Since we are given the position, we can convert it to velocity by differentiating it with respect to time,
Hence, v = dx/dt = d(Ate-Bt)/dt = d(Ate)/dt - d(Bt)/dt = Aedt/dt - Bdt/dt = Ae-B
When velocity is zero (electron at momentary stop):
v = Ae-B = 0 or, e = B/A
We can substitute the value of e in the equation of position (x),
x = Ate-Bt = At(B/A) - Bt = Bt - Bt = 0.
Since electron is moving along x-axis, x= 0 refers to the origin.
Hence the given electron is at origin itself, when it stops momentarily.
Hope this helps.