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.style="color: rgb(64, 64, 64); font-family: arial, helvetica, sans-serif; font-size: 13px; line-height: 15.359375px;">style="color: rgb(64, 64, 64); font-family: arial, helvetica, sans-serif; font-size: 13px; line-height: 15.359375px;">style="color: rgb(64, 64, 64); font-family: arial, helvetica, sans-serif; font-size: 13px; line-height: 15.359375px;">style="color: rgb(64, 64, 64); font-family: arial, helvetica, sans-serif; font-size: 13px; line-height: 15.359375px;">style="color: rgb(64, 64, 64); font-family: arial, helvetica, sans-serif; font-size: 13px; line-height: 15.359375px;">style="color: rgb(64, 64, 64); font-family: arial, helvetica, sans-serif; line-height: 15.359375px;">style="color: rgb(64, 64, 64); font-family: arial, helvetica, sans-serif; font-size: 13px; line-height: 15.359375px;">style="color: rgb(64, 64, 64); font-family: arial, helvetica, sans-serif; line-height: 15.359375px;">style="color: rgb(64, 64, 64); font-family: arial, helvetica, sans-serif; font-size: 13px; line-height: 15.359375px;">style="color: rgb(64, 64, 64); font-family: arial, helvetica, sans-serif; font-size: 13px; line-height: 15.359375px;">style="color: rgb(64, 64, 64); font-family: arial, helvetica, sans-serif; font-size: 13px; line-height: 15.359375px;">

Here r is in meters and t is in seconds. Consider only when t > 0.>style="color: rgb(64, 64, 64); font-family: arial, helvetica, sans-serif; font-size: 13px; line-height: 15.359375px;">style="color: rgb(64, 64, 64); font-family: arial, helvetica, sans-serif; font-size: 13px; line-height: 15.359375px;">

style="color: rgb(64, 64, 64); font-family: arial, helvetica, sans-serif; font-size: 13px; line-height: 15.359375px;">

(a) What is the velocity vector for the electron (written in unit vector notation, with i and j)?style="color: rgb(64, 64, 64); font-family: arial, helvetica, sans-serif; font-size: 13px; line-height: 15.359375px;">style="color: rgb(64, 64, 64); font-family: arial, helvetica, sans-serif; font-size: 13px; line-height: 15.359375px;">style="color: rgb(64, 64, 64); font-family: arial, helvetica, sans-serif; font-size: 13px; line-height: 15.359375px;">style="color: rgb(64, 64, 64); font-family: arial, helvetica, sans-serif; font-size: 13px; line-height: 15.359375px;">style="color: rgb(64, 64, 64); font-family: arial, helvetica, sans-serif; font-size: 13px; line-height: 15.359375px;">

(b) When, if ever, is the velocity zerostyle="color: rgb(64, 64, 64); font-family: arial, helvetica, sans-serif; font-size: 13px; line-height: 15.359375px;">

(c) What is the acceleration vector for the electron? (Again in unit vector notationstyle="color: rgb(64, 64, 64); font-family: arial, helvetica, sans-serif; font-size: 13px; line-height: 15.359375px;">

(d) When (if ever) is the acceleration zero?style="color: rgb(64, 64, 64); font-family: arial, helvetica, sans-serif; font-size: 13px; line-height: 15.359375px;">

(e) When (if ever) does the speed equal 10m/s?style="color: rgb(64, 64, 64); font-family: arial, helvetica, sans-serif; font-size: 13px; line-height: 15.359375px;">

Explanation / Answer

a)dr/dt=(6t-3t^2)i+8j

b)sqrt((6t-3t^2)^2+64)=0

find t

c)d^2 r/dt^2=(6-6t)i

d)acceleration is 0

6-6t=0

t=1sec

e)sqrt((6t-3t^2)^2+64)=10

find t

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