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
Mar 16, 2016

Answer:

#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#