What is the average speed of an object that is still at #t=0# and accelerates at a rate of #a(t) = 12-3t# from #t in [0, 4]#?

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Answer 1 · 2017-08-03T09:12:26

The average speed is #=16ms^-1#

The speed is the integral of the acceleration

#a(t)=12-3t#

#v(t)=int(12-3t)dt=12t-3/2t^2+C#

Plugging in the initial conditions, #v(0)=0#

Therefore,

#0=0-0+C#

So,

#v(t)=12t-3/2t^2#

The average speed is

#4barv=int_0^4(12t-3/2t^2)dt=[12/2t^2-1/2t^3]_0^4#

#=(96-32)-(0)=64#

#barv=64/4=16ms^-1#