What is the average speed of an object that is moving at #12 m/s# at #t=0# and accelerates at a rate of #a(t) =7-t# on #t in [0,4]#?

1 Answer
Gió
Mar 3, 2016

I found #5m/s#

Explanation:

I do not want to complicate it too much but I would integrate the acceleration to go back to the expression of velocity:
#v(t)=inta(t)dt=int(7-t)dt=7t-t^2/2+c#
now we get the constant #c# by imposing that at #t=0# we have #v(0)=12m/s#. So:
#12=(7*0)-(0)^2/2+c#
so that #c=12m/s#
so the velocity will be:
#v(t)=7t-t^2/2+12#
that at #t=4s# is:
#v(4)=(7*4)-(4^2)/2+12=32m/s#

Average speed will be: #(Deltav)/(Deltat)=(v(4)-v(0))/(4-0)=(32-12)/4=5m/s#

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