What is the average speed of an object that is moving at #22 m/s# at #t=0# and accelerates at a rate of #a(t) =t-2# on #t in [0,2]#?
Since average speed is given by the equation
we need to find the position of the object at times
Since no initial position is given, we'll assume its position at
We're given an equation for how the object's acceleration varies with time, and what we need to find is how its position varies with time, so we can find its position at time
The velocity equation for the object is
And the position equation with respect to time is
Which, after simplifying, yields
Lastly, let's calculate the average velocity, using our first equation:
Rounded to two significant figures.