What is the average speed of an object that is moving at #9 m/s# at #t=0# and accelerates at a rate of #a(t) =2t+1# on #t in [1,2]#?

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Answer 1 · 2018-03-02T09:26:12

The average speed is #=12.83ms^-1#

The speed is the integral of the acceleration

#a(t)=2t+1#

#v(t)=int(2t+1)dt#

#=t^2+t+C#

Plugging in the initial conditions

#v(0)=9#

#v(0)=0+C=9#

#=>#, #C=9#

Therefore,

#v(t)=t^2+t+9#

The average speed is

#(2-)barv=int_1^2(t^2+t+9)dt#

#barv=[t^3/3+t^2/2+9t]_1^2#

#=(8/3+2+18)-(1/3+1/2+9)#

#=7/3+11-1/2#

#=12.83ms^-1#