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

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Answer 1 · 2017-07-16T15:13:19

The average speed is #=-0.5ms^-1#

The speed is the integral of the acceleration

#a(t)=3t-4#

#v(t)=int(3t-4)dt=3/2t^2-4t+C#

Plugging in the initial conditions at #t=0#

#v(0)=0-0+C=0#, #=>#, #C=0#

The average velocity is

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

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

#=(27/2-18)-(4-8)#

#barv=-0.5#