While it's perfectly fine to let a dedicated navigation device or smartphone application tell us how to drive, let's see how (one-dimensional) motion can be described in physics.
We'll use that scary word--calculus--but just to motivate the connections between different types of motion graphs.
We can connect these three key quantities--position, velocity, and acceleration--in a "calculus chain of pain," where we move to the left by differentiation, or move to the right by integrating. While we don't need to explicitly evaluate these operations in an algebra-based college physics course...
Let's try to utilize the "chain of pain" in answering these types of questions:
The __________ gives the displacement of an object.
(A) chord slope of an x(t) graph.
(B) tangent slope of an x(t) graph.
(C) chord slope of a vx(t) graph.
(D) tangent slope of a vx(t) graph.
(E) area under a vx(t) graph.
(F) area under an ax(t) graph.
(G) (None of the above choices.)
(H) (Unsure/guessing/lost/help!)
The chord slope of a vx(t) graph gives the __________ of an object.
(A) displacement.
(B) position.
(C) change in (instantaneous) velocity.
(D) (instantaneous) velocity.
(E) average velocity.
(F) (instantaneous) acceleration.
(G) average acceleration.
(H) (None of the above choices.)
(I) (Unsure/guessing/lost/help!)
Now let's consider the equations used to describe motion.
This "list of five" motion equations seems overwhelming, and the temptation is to use them willy-nilly, or by picking one arbitrarily without knowing whether/why it would happen to work. Which leads us to Will Ferrell in Elf (New Line Cinema, 2003), picking gum off of a railing. Sure, it may taste good, and it costs you nothing, but in physics as with found street gum, an equation you pick up without knowing or understanding where it came from is usually not going to turn out well. So later let's look at the most important part of solving physics problems--reading through and picking out the known/given/inferred quantities, identifying the remaining unknown quantities, and then this will help you determine just equation(s) you should be using for a particular situation.
(Hat tip to Rhett Allain, "Don’t Eat Candy You Find on the Ground," Wired Dot Physics, June 24, 2011 for the Elf reference.)
No comments:
Post a Comment