Basics About Motion Weve Gotta Keep Movin Lets

Basics About Motion We’ve Gotta Keep Movin’

Let’s just take a moment to mention vectors § A vector is a quantity that has magnitude (size) and direction § It is represented with an arrow ( a ray) § A scalar is a quantity without direction (time, mass)

Definitions § Displacement versus distance: from here to there § Velocity versus speed: rate of position change § Acceleration: rate at which velocity changes

Some Basic Thoughts § Displacement is represented by “s” § Velocity is…… § A brief aside for a little calculus § So, average velocity and instantaneous velocity… § Nothing much to say about that § Vave = Ds/Dt § Vinst = lim Ds/Dt Dt 0 § Be careful which velocity we’re talking about.

So, let’s decide what some basic formulas might look like § How does displacement relate to velocity? § How does acceleration relate to velocity? § Velocity is the change in position (displacement) over time: v = (sf –si )/t § Acceleration is change in velocity over time : a = (vf -vi)/t

Looking at simple motion graphs to see concepts § Displacement § Velocity (changing (position) versus time: graph: where you’re going are and when § General shape and what it tells us § Specific slope and what it tells us § Positive and negative values § Accelerating motion § General shape and what it tells us § Positive and negative § Slope and area

Position versus time graphs (Constant Velocity) § Calculate the slope of this line. § Calculate the area under the curve from t= 0 to t= 10 § Since velocity is Ds/Dt it will be the ? of this curve?

Position versus Time Graph (Changing Velocity) § Find a slope at t = 5 seconds § Find slope at t 8 seconds § Average vs. Instant. § Predict an area under a curve from t = 2 to t = 8

Now, Analyze This § Questions to consider: -What is happening to the position of this? -How is it moving? -What is the slope? -Is it changing?

And, this § Questions to consider: -What is happening to the position of this? -How is it moving? -What is the slope? -Is it changing?

And, finally § Questions to consider: -What is happening to the position of this? -How is it moving? -What is the slope? -Is it changing?

So, what about acceleration? § Acceleration is the rate at which the velocity changes § This includes directional changes § a = Dv/Dt § Another way of expressing this isvf = vi + a t

Velocity versus time graph § Find the slope § What would it represent? § Find the area under the curve § What would it represent?

Summary of relationships § § § Vave = Ds/Dt Vave = (vf + vi)/2 Vf = v i + a t S = vi t + ½ a t 2 V f 2 – v i 2 = 2 a s