What is the average speed of an object that is moving at #3 m/s# at #t=0# and accelerates at a rate of #a(t) =t^2-1# on #t in [0,2]#?

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Answer 1 · 2017-05-08T12:21:21

The average speed is #=2.67ms^-1#

The speed is the integral of the acceleration

#a(t)=t^2-1#

#v(t)=int(t^2-1)dt#

#v(t)=1/3t^3-t+C#

Plugging in the initial conditions

#v(0)=0-0+C=3#

So,

#C=3#

and

#v(t)=1/3t^3-t+3#

The average speed is

#2barv=int_0^2(1/3t^3-t+3)dt#

#=[1/12t^4-1/2t^2+3t]_0^2#

#=(16/12-4/2+6)-(0)#

#=16/3#

#barv=(16/3)/2=2.67ms^-1#