What is the average speed of an object that is still at #t=0# and accelerates at a rate of #a(t) = 6-t# from #t in [0, 2]#?

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Answer 1 · 2017-04-06T06:15:01

The average speed is #=5.33ms^-1#

The velocity is the integral of the acceleration

#a(t)=6-t#

#v(t)=int(6-t)dt#

#=6t-t^2/2+C#

We apply the initial conditions to find #C#

#v(0)=0#

Therefore, #C=0#

So,

#v(t)=6t-t^2/2#

We can calculate the average value of the velocity

#(2-0)barv=int_0^2(6t-t^2/2)dt#

#=[3t^2-t^3/6]_0^2#

#=(12-4/3)-(0)#

#=32/3#

#=10.67#

So,

#barv=10.67/2=5.33ms^-1#