An electron\'s position is given by [ModifyingAbove r With right-arrow equals 3

Q: An electron's position is given by [ModifyingAbove r With right-arrow equals 3

postion equation for electron is given by x = 3ti + 4t^2 j + 2k x component = 3t y component = 4t^2 z component = 2 speed V = dx/dt = d( 3ti + 4t^2 j + 2k )/dt V = 3 i + 8 t j + 0 so x component of speed = 3 y component of speed = 8t and z component of speed = 0 -------------------------------------------- spped of eelctron = V^2 = 3^2 + 8^2 t^2 V = sqrt(9 + 64 t^2 ) ------------------------------- angle tan theta = y/x = 8t/3 = 2.67 t

ID: 1406681 • Letter: A

Question

An electron's position is given by [ModifyingAbove r With right-arrow equals 3 t ModifyingAbove i With caret plus 4 t squared ModifyingAbove j With caret plus 2 ModifyingAbove k With caret] , where t is in seconds and [ModifyingAbove r With right-arrow] is in meters. What are the (a) x-, (b) y- and (c) z-components of the electron's velocity? (d) What is the electron's speed? (e) What angle does the electron's velocity make with positive x-axis? Give all answers as appropriate functions of time.

Explanation / Answer

postion equation for electron is given by

x = 3ti + 4t^2 j + 2k

x component = 3t

y component = 4t^2

z component = 2

speed V = dx/dt = d( 3ti + 4t^2 j + 2k )/dt

V = 3 i + 8 t j + 0

x component of speed = 3

y component of speed = 8t

and z component of speed = 0

--------------------------------------------

spped of eelctron = V^2 = 3^2 + 8^2 t^2

V = sqrt(9 + 64 t^2 )

-------------------------------

angle tan theta = y/x = 8t/3 = 2.67 t

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An electron\'s position is given by ModifyingAbove r With right-arrow equals 3 t

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An electron\'s position is given by [ModifyingAbove r With right-arrow equals 3

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