What is the average speed of an object that is moving at #12 m/s# at #t=0# and accelerates at a rate of #a(t) =2-3t^2# on #t in [0,2]#?

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Answer 1 · 2017-07-13T06:05:40

The average speed is #=12ms^-1#

The speed is the integral of the acceleration

#a(t)=2-3t^2#

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

Plugging in the initial conditions at #t=0#

#v(0)=0-0+C=12#, #=>#, #C=12#

So,

#v(t)=2t-t^3+12#

The average speed is

#2barv=int_0^2(2t-t^3+12)dt#

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

#=(4-4+24)-(0)#

#barv=24/2=12#

The average speed is #barv=12ms^-1#