Acceleration

Anything that moves (and this means anything from blades of grass to rockets), has speed and we can calculate it. 

                                              Speed = distance/time 


If we give a speed in a given direction, we'll have an objects velocity.


                                       Velocity = distance/time  in a direction

More importantly, a change in velocities will give us an objects acceleration.

                       acceleration = final velocity - initial velocity
                                                              time




Some questions that often throw students are these:


1. When an object slows down, does it accelerate or decelerate?


2. If we use final velocity minus initial velocity of an object that starts from a stop and then ends at a stop, isn't the answer going to be zero and show no movement?


3. How can math possibly show what's happening? I know because I can see it with my eyes.



Recently, we pushed each other on scooters, dropped markers at one second intervals, came to complete stop and then measured the distance between those markers. We made a diagram like this to record our results:

We can use this information to easily calculate the scooter/student's speed:

Say, we can calculate acceleration now! If we use final velocity, the object ending at a complete stop (0 ft/sec), minus initial velocity, the object starting at a complete stop  (0 ft/sec), divided by the entire time, mathematically, you'll get 0. This is the objects average acceleration and it doesn't give you as much information about what actually happened. Using average acceleration shows that the average acceleration was zero, but we can clearly see that the object did accelerate, so average acceleration does not give the whole picture. (answer to question #2 above)

So how can we get the whole picture and show actually what happened?


We use instantaneous acceleration to show what happened each second the object was moving. Here's the diagram now:

When we look at each acceleration, it's easy for us to see that they're positive and negative acceleration. 

A positive acceleration means that the object was speeding up, a negative acceleration means the object is slowing down. There is no deceleration!!! We call it, negative acceleration. (answer to question #1 above)


When we look at these accelerations, we're able to prove, mathematically, exactly when the object sped up, for how long, slowed down, and came to a stop. (answer to question #3 above)

I've started this blog as a way for current students, their parents, my co-workers and administrators to have a window into my classroom. It isn't a platform to highlight my personal views or ideas.  I want it to be a place for students to be able to review what we've covered, have a place where they can share that information with their parents, and as a passive way for parents to be able to keep abreast with what we're doing. I hope that this becomes the helpful teaching tool that I want it to be. I believe for that to happen, though, I will need the help of current and former students, parents, co-workers, and administrators. This blog will only be useful, if it's used. So, here's to something new, to high hopes, and to those that matter most--my students.