What is the average speed of an object that is moving at #5 m/s# at #t=0# and accelerates at a rate of #a(t) =t-4# on #t in [4,5]#?

1 Answer
May 11, 2016

Answer:

#v_a=17/6" " m/s#

Explanation:

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

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

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

#v=int (t-4)*d t#

#v=t^2/2-4t +C " "t=0 ;v=5 m/s" ; "c=5 m/s#

#v=t^2/2-4t+5#

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

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

#int d x=int _4^5 v(t)*d t#

#x=int_4^5 (t^2/2-4t+5)d t#

#x=|1/2*t^3/3-4*t^2/2+5*t|_4^5#

#x=(1/2*5^3/3-2*5^2+5*5)-(1/2*4^3/3-2*4^2+5*4)#

#x=125/6-50+25)-(64/6-32+20)#

#x=125/6-25-64/6+12=61/6-13#

#x=(61-78)/6#

#x=|-17/6|#

#x=17/6 meters#

#v_a=x/t#

#v_a=(17/6)/(5-4)#

#v_a=17/6" " m/s#