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) =5-3t# on #t in [0,4]#?

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Answer 1 · 2017-05-04T10:10:06

The average speed is #=6.5ms^-1#

The speed is the integral of the acceleration

#a(t)=5-3t#

#v(t)=int(5-3t)dt#

#v(t)=5t-3/2t^2+C#

Plugging in the initial conditions

#v(0)=0-0+C=12#

So,

#C=12#

and

#v(t)=5t-3/2t^2+12#

The average speed is

#4barv=int_0^4(5t-3/2t^2+12)dt#

#=[5/2t^2-3/6t^3+12t]_0^4#

#=(10-32+48)-(0)#

#=26#

#barv=26/4=6.5ms^-1#