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

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.

i have found everything else i need help working on the degree on part E

Explanation / Answer

Here, the i, j and k all denote unit vectors in the x y and z direction respectively
velocity= dr/dt (time derivative of position)
v=dr/dt=3 i + 8t j + 0k

a) 3
b) 8t
c) 0
d) speed = magnitude of velocity
speed=sqrt(Vx²+Vy²+Vz²)
=sqrt(3² + (8t)² +0²)
=sqrt(9+64t²)
e)tan(angle)=y/x
angle=arctan(y/x)
=arctan(8t/3)

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