What is the average speed of an object that is still at #t=0# and accelerates at a rate of #a(t) = 5t+1# from #t in [0, 6]#?
1 Answer
Explanation:
To find the average speed of the object, we have to know both the total distance traveled (
We need to integrate this acceleration equation in order to find the position equation. The integral of
Doing the same for the second quantity (
Therefore, the first integral of the acceleration equation, which is the velocity equation, is
because the initial velocity and position are assumed to be
Since this is the velocity equation, we need to integrate this again to find the position equation. Following the same procedure as before, our result is
Now that we have our position equation, let's find the position of the particle at the time
Since the velocity and position are always increasing here, the average speed is the same as the average velocity, which is given by the equation
Since our initial position and time are both