Class started with a quick touch on last week’s topic, and we looked at a few more ways to calculate the circumference of the earth. The professor told an interesting story about how at the mid summer solstice in Egypt, you could look into a well and see the sun rays reaching the bottom, while at another location towards the north the rays did not quite reach the bottom. From there the Ancient Greek’s (Living in Alexandria Egypt…) were able to calculate the circumference of the earth.
But onto this Week! Chapter 2 is on the study of motion, more particularly on the study of Kinematic motion, which I think is motion in one dimension only. (Along the x-axis for our purposes).
Average Speed: Distance covered / Time to cover the distance
Speed DOES NOT care about direction.
If you assume your object is moving in a straight line from one point (x1) to another point (x2) and it left point one at time (t1) and arrived at the second point (t2) you can say: Average Speed = x2 – x1 / t2 – t1
This neat Average Speed goes out the window if your object does not cooperate and instead zooms to various points other points along the way from x1 to x2. Then you need to get the total distance traveled across the zooming paths and divide by the time taken to zoom around.
An interesting example was if first you go 60 miles in 1 hour and then go 60 miles in 2 hours, what is your Average speed? It is 40, since you need to calculate the total miles traveled (120 miles) over the total time taken (3 hours). So Average Speed from two known average speeds needs to be a weighted average.
(Note: Can be written v with little line on top or
Average Velocity only cares about your start location and your stop location. It also shows direction, from the origin. Negative #’s are west of the origin, Positive #’s are east of the origin. Velocity is expressed as a vector.
If you spend three hours driving in a loop, only to end up back where you started your average velocity is ZERO.
This is similar to Average Velocity, except you want to take shorter and shorter intervals in time. So if Average Velocity = x2 – x1 / t2-t1 = Δx/Δt
Instantaneous Velocity is The Average Velocity as the t approach’s Zero. This is the first sign of calculus in the course.
Read this as The Instantaneous Velocity is the Change in x (distance) over the change in t (time) as the time becomes close to 0.
The professor also said this is equal to the derivative of x over the derivative of t. But I’m not to sure about derivatives yet. I will read about them and write a quick post.