The position of an electron moving in the xy plane is given by r = (3.0t 2 - t 3

Question

The position of an electron moving in the xy plane is given by r = (3.0t2 - t3)i + (8.0 + 8.0t)j. Here r is in meters and t is in seconds. Consider only when t > 0.

(a) What is the velocity vector for the electron (written in unit vector notation, with i and j)?

(b) When, if ever, is the velocity zero?

(c) What is the acceleration vector for the electron? (Again in unit vector notation.)

(d) When (if ever) is the acceleration zero?

(e) When (if ever) does the speed equal 10m/s?

P.S. - For full points, please show any and all work involved (I'm mostly confused on b) and e) soooo yeah! :))

Explanation / Answer

a) v = dr/dt   = (6t - 3t^2)i + 8j  

b) no , the v = (6t - 3t^2)i + 8j will always be greater than 8 m/s .

c) a = dv/dt =( 6 - 6t ) i

d) yes at t = 1 sec

e) |v|   = srt[ (6t - 3t^2)^2 + 8^2] = 10

t = 2.73 sec

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