What is the average speed of an object that is not moving at #t=0# and accelerates at a rate of #a(t) =8-t# on #t in [2,5]#?

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Answer 1 · 2017-11-25T07:12:55

The average speed is #=21.5ms^-1#

The speed is the integral of the acceleration

#a(t)=8-t#

#v(t)=int(8-t)dt=8t-1/2t^2+C#

Plugging in the initial conditions

#v(0)=0#

so,

#v(0)=8*0-1/2*O+C=0#

#C=0#

#v(t)=8t-1/2t^2#

The average speed on the interval #t in [2,5]# is

#(5-2)barv=int_2^5(8t-1/2t^2)dt#

#3barv=[8/2t^2-1/6t^3]_2^5#

#3barv=(4*25-1/6*125)-(4*4-1/6*8)#

#3barv=84-125/6+4/3=64.5#

#barv=64.5/3=21.5ms^-1#