Acceleration Part 2: Learning Objective: Derive general equation of motion for a particle under constant acceleration. Extend derivation to time independent formula for distance and velocity. Contains Keynote (power point) presentation.
CA content standards: Physics 1c
Students know how to apply the law F=ma to solve one-dimensional motion problems that involve constant forces (Newton’s second law).
Analyze data to support the claim that Newton’s second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration. [Clarification Statement: Examples of data could include tables or graphs of position or velocity as a function of time for objects subject to a net unbalanced force, such as a falling object, an object rolling down a ramp, or a moving object being pulled by a constant force.] [Assessment Boundary: Assessment is limited to one-dimensional motion and to macroscopic objects moving at non-relativistic speeds.]
Learning Objective: Learn to derive the general equation of motion for a particle under constant acceleration, and to extend the derivation to time independent formula for distance and velocity. (uses the 2 column derivation method)
This may be your first introduction to the art of deriving formulas, so I’ll start by explaining the 2 column derivation method.
STEP 1: THIS IS AN ALWAYS !!!!
Draw a quick sketch of the physical situation or a graph.
Step 2:Define variables, knowns and unknowns, identify general formulas etc.(In later lessons, you’ll also be drawing “free body diagrams” – more on that later).
NEXT STOP: DERIVATION STATION !!!!
The 2 column derivation method is something I learned in graduate school. It will help you separate math errors from logical errors. This method may remind you of the dreaded deductive logic proofs you learned in geometry. But this is different. In geometry you may make a math statement and justify the step with a reason (example: 2 triangles are congruent, reason: Side Angle Side). In the 2 column derivation method, you decide your next step in the right hand column, then do the math in the left hand column. If you made an error, you can easily check your math steps separately from your logic. Believe me – using this method will save you thousands of hours of frustration!
First you need to set up a 2 column table;
|math statement of goal||goal|
|math steps||steps to do|
See Keynote Presentation: