What is the average speed of an object that is moving at 4 m/s at t=0 and accelerates at a rate of a(t) =2t^2-2t+4 on t in [0,3]?

1 Answer
ali ergin
Mar 16, 2016

v_a=11,5 " "m/s

Explanation:

v(t)=int (2t^2-2t+4) d t
v(t)=2/3t^3-2/2t^2+4t+C" for t=0 v=4 m/s C=4"
v(t)=2/3 t^3-t^2+4t+4
Delta x=int_0^3 (2/3 t^3-t^2+4t+4)d t
Delta x=|2/3*1/4 t^4-1/3 t^3+4/2t^2+4t|_0^3
Delta x=(1/6*81-27/3+2*9+4*3)-0
Delta x=27/2-9+18+12" "Delta x=27/2+21
Delta x=(42+27)/2
Delta x=69/2 " "Delta x=34,5 m
Delta x":displacement at interval (0,3)"
v_a=(Delta x)/(Delta t)
v_a=(34,5)/(3-0)
v_a=(34,5)/3
v_a=11,5 " "m/s

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