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

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Answer 1 · 2017-12-31T13:05:18

The average speed is #=1.5ms^-1#

The speed is the integral of the acceleration

#a(t)=t#

Therefore,

#v(t)=inta(t)dt=inttdt=t^2/2+C#

Plugging in the initial conditions

#v(0)=0#

#v(0)=0+C#, #=>#, #C=0#

Therefore,

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

The average speed in the interval #t in [0, 3]# is

#3 barv=int_0^3t^2/2dt=[t^3/6]_0^3=(27/6)-(0)#

#barv=9/6=3/2=1.5ms^-1#