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-5# on #t in [1,4]#?

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Answer 1 · 2017-04-01T05:40:25

The average speed is #=3.5ms^-2#

#a(t)=2t-5#

The speed is the integral of the acceleration

#v(t)=int(2t-5)dt#

#v(t)=2/2t^2-5t+C#

Initial conditions are,

#v(0)=9#

Therefore,

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

So,

#v(t)=t^2-5t+9#

The average velocity is #barv#

#(4-1)barv=int_1^4(t^2-5t+9)dt#

#3barv=[t^3/3-5/2t^2+9t]_1^4#

#=(64/3-40+36)-(1/3-5/2+9)#

#3barv=52/3-41/6=63/6=21/2#

#barv=7/2ms^-1#