What is the average speed of an object that is not moving at #t=0# and accelerates at a rate of #a(t) =5t-10# on #t in [3, 5]#?

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Answer 1 · 2016-05-11T21:11:23

#v_a=51.25 m/s#

#(d v)/(d t)=a(t)#

#d v=a(t)*d t#

#int d v=int a(t) *d t#

#v=int(5t-10) *d t#

#v=5*t^2/2-10*t+C#

#t=0 rarr v=0 rarrc=0#

#v=5/2 t^2-10t#

#v_a=1/(5-3)int_3^5 |(5/2 t^2-10t)|d t#

#v_a=1/2[|5/2*t^3/3-10*t^2/2|_3^5]#

#v_a=1/2[(5/2*5^3/3-5*5^2)-(5/2*3^3/3-5*3^2)]#

#v_a=1/2[(625/6-125)-(45/2-45)]#

#v_a=1/2[(625-750)-(-45/2)]#

#v_a=1/2[-125+45/2]#

#v_a=|-51.25 |#

#v_a=51.25 m/s#