# 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]#?

##### 1 Answer

#### Explanation:

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 *velocity* equation, then integrating that to find its position equation. If you're not familiar with integrals, just know that the integral of

The velocity equation for the object is

And the position equation with respect to time is

Which, after simplifying, yields

Plugging in

Lastly, let's calculate the average velocity, using our first equation:

Rounded to two significant figures.