An object's two dimensional velocity is given by #v(t) = ( t-1/t, t^2)#. What is the object's rate and direction of acceleration at #t=3 #?

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Answer 1 · 2017-01-13T09:39:58

The acceleration is #=〈10/9,6〉# and the direction is #=79.5#º

#v=〈t-1/t,t^2〉#

Acceleration is

#a(t)=(dv)/dt=〈1+1/t^2,2t〉#

Therefore,

#a(3)=〈1+1/9,6〉=〈10/9,6〉#

The direction is #=arctan(6/(10/9))#

#=arctan(54/10)=79.5#º