What is the average speed of an object that is still at #t=0# and accelerates at a rate of #a(t) = t/4+1# from #t in [0, 6]#?

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Answer 1 · 2017-11-11T01:40:28

"Average" velocity is just the arithmetic mean of the initial and final velocities.
#v_(avg) = 7.5#

#"Acceleration" = ("Velocity")/("time")#

#a(t) = t/4 + 1# ; #v/t = t/4 + 1#

#v = t^2/4 + t#

#v_0 = 0#; #v_6 = 6^2/4 + 6 = 36/4 + 6 = 15#

#(v_6 - v_0)/2 = 7.5#