What is the average speed of an object that is moving at #8 m/s# at #t=0# and accelerates at a rate of #a(t) =5-6t# on #t in [0,2]#?

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Answer 1 · 2017-06-04T07:12:29

The average speed is #=9ms^-1#

The speed is the integral of the acceleration

#a(t)=5-6t#

#v(t)=int(5-6t)dt#

#v(t)=5t-6/2t^2+C#

#v(t)=5t-3t^2+C#

Plugging in the initial conditions

#v(0)=0-0+C=8#

So,

#C=8#

and

#v(t)=5t-3t^2+8#

The average speed is

#2barv=int_0^2(5t-3t^2+8)dt#

#=[5/2t^2-3/3t^3+8t]_0^2#

#=(10-8+16)-(0)#

#=18#

#barv=(18)/2=9ms^-1#