An ion\'s position vector is initially [r Overscript right-arrow EndScripts equa

Question

An ion's position vector is initially [r Overscript right-arrow EndScripts equals left-parenthesis -8.2 m right-parenthesis i Overscript EndScripts plus left-parenthesis 8.0 m right-parenthesis j Overscript EndScripts plus left-parenthesis -1.9 m right-parenthesis k Overscript EndScripts] , and 5.6 s later it is [r Overscript right-arrow EndScripts equals left-parenthesis 2.7 m right-parenthesis i Overscript EndScripts plus left-parenthesis -4.2 m right-parenthesis j Overscript EndScripts plus left-parenthesis 4.8 m right-parenthesis k Overscript EndScripts] . In unit-vector notation, what is its average velocity during the 5.6 s?

Explanation / Answer

given

rfinal = -8.2 i + 8 j - 1.9 k

rinitial = 2.7 i - 4.2 j + 4.8 k

r = rfinal - rinitial

r = - 10.9 i + 12.2 j - 6.7k

and given t = 5.6 s

the velcoity is = the distance of the vector / time

= (- 10.9 i + 12.2 j - 6.7k ) / 5.6

= - 1.94 i + 2.17 j - 1.196 k

average magnitude of the velocity is = ( 1.942 + 2.172 + 1.1962 )1/2

= 2.75 m/s

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