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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?

Question

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?

check_circleAnswer
Step 1

Given:

Position of electron on x-axis, x = Ate-Bt

A and B are the postive constants.

Step 2

Calculating the velocity of the electron:

Position of electron on x-axis is given as, x
Ate5t.... .(1)
dx
As we know, v=-
dt
d(Ate (At){(-B)#} +(4c"#){}
Using x from equation (1)
y=
dt
v=(AeB") {1-Bi. ..2)
V
help_outline

Image Transcriptionclose

Position of electron on x-axis is given as, x Ate5t.... .(1) dx As we know, v=- dt d(Ate (At){(-B)#} +(4c"#){} Using x from equation (1) y= dt v=(AeB") {1-Bi. ..2) V

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Step 3

Calculating the time at which the electron momentarily stops:

To s...

Putting equation (2) equal to zero, we get,
v(Ae B){1-Br0
(1-Br) 0
Or t
(3)
help_outline

Image Transcriptionclose

Putting equation (2) equal to zero, we get, v(Ae B){1-Br0 (1-Br) 0 Or t (3)

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