An object's two dimensional velocity is given by #v(t) = ( t-2 , 5t^2-3t)#. What is the object's rate and direction of acceleration at #t=7 #?

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Answer 1 · 2017-03-07T14:40:45

#"acceleration"=(1,67)=(veci+67vecj)ms^(-2)#

direction#=tan^(-1)67#with x-axis

If we are given velocity as a function of time, the acceleration is found by differentiating that function.

ie. #" "a(t)=dotv(t)=(d(v(t)))/(dt)#

#v(t)=(t-2,5t^2-3t)#

#a(t)=dotv(t)=(1,10t-3)#

#a(7)=(1,70-3)=(1,67)=(veci+67vecj)ms^(-2)#

direction#tan^(-1)(67/1)=tan^(-1)67# with x-axis