What is the average speed of an object that is still at #t=0# and accelerates at a rate of #a(t) =2t^2-t-4# from #t in [2, 3]#?

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Answer 1 · 2017-03-24T07:44:27

The average speed is #=6.17ms^-1#

#a(t)=2t^2-t-4#

Velocity is

#v(t)=int(2t^2-t-4)dt#

#=2/3t^3-1/2t^2-4t+C#

Initial conditions, #v(0)=0#

#v(0)=0+C=0#

So,

#C=0#

Average speed is

#barv*(3-2)=int_2^3(2t^2-t-4)dt#

#=[2/3t^3-1/2t^2-4t]_2^3#

#=(18-9/2-12)-(16/3-2-8)#

#=6-9/2-16/3+10#

#=16-59/6#

#=37/6#

The average speed is #=6.17ms^-1#