# What is the average speed, on #t in [0,5]#, of an object that is moving at #8 m/s# at #t=0# and accelerates at a rate of #a(t) =5t^2-2t# on #t in [0,3]#?

The average speed is

The speed is the integral of the acceleration

Plugging in the initial conditions

Therefore,

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The average speed is 31 m/s.

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