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) =3-t# on #t in [0,5]#?

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Answer 1 · 2018-05-07T14:35:01

The average speed is #=12.33ms^-1#

#a(t)=3-t#

The velocity is the integral of the acceleration

#v(t)=inta(t)dt=int(3-t)dt=3t-1/2t^2+C#

Plugging in the initial conditions

#v(0)=9#

Therefore,

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

#C=9#

#v(t)=3t-1/2t^2+9#

The average speed on #t in [0,5]# is

#(5-0)barv=int_0^5(3t-1/2t^2+9)dt#

#(5)barv=[3/2t^2-1/6t^3+9t]_0^5#

#=(75/2-125/6+45)-(0)#

#=185/3#

#barv=185/15=12.33ms^-1#