What is the average speed, on #t in [0,5]#, of an object that is moving at #10 m/s# at #t=0# and accelerates at a rate of #a(t) =2t^2-10# on #t in [0,3]#?

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Answer 1 · 2017-08-06T06:46:00

The average speed is #=1.6ms^-1#

The speed is the integral of the acceleration

#a(t)=2t^2-10#

#v(t)=2/3t^3-10t+C#

Plugging in the initial conditions

#v(0)=0-0+C=10#

Therefore,

#v(t)=2/3t^3-10t+10# on the interval #I=[0,3]#

The total distance travelled in #5s# is

#d=int_0^3(2/3t^3-10t+10)dt+v(3)*2#

#=[1/3t^4-5t^2+10t]_0^3+(18-30+10)*2#

#=(27-45+30)+(-4)#

#=8#

The average speed is

#barv=8/5=1.6ms^1#