Embedded Files
Importance of :
points
Slope
area under curve
Types of graphs / relationships in DP Physics:
square relationship -
square root
inverse (radical)
inverse square
sine - linear Snell's law data
Importance of Area Under the Curve
Importance of Area Under the Curve
(the most basic idea behind integrals)
Suppose you were to be paid a certain amount of money [y] for working 1 hour [$/hr]. If you worked x hours, the calculation of your total earnings would be as shown in the graph.
If you were to work twice as long (x_2), you would simply earn twice as much as shown above.
The area under the curve on this graph would represent ($).
While the units (meaning) of the area may change for each graph, the process to determine the area remains consistent.
In many professions your pay increases as you gain more experience. Suppose that your wage ($/hr) were to increase at a constant rate. While initially this may not seem like a good deal, it may pay off in the long run.
During the same time of x_1, you would only make 50% of the original amount, however this will change.
In this scenario, if you now worked for x_2 hours, you would double not only the number of hours but ALSO the amount of your pay.
The triangle formed by the graph grows in BOTH length and height. Therefore, the area is now 4x the original size (as shown by the shaded triangles).
We could then say that the pay was proportional to the square of the time.
when y is also influenced by x.
This can summarized mathematically as shown to the left. If the RATE at which the wages increases is known, the slope of the graph ($/hr/hr). This information can then be used to create a generalized equation as shown.
We will use this concept / procedure throughout the course. Each time we will substitute different variables for x, y, A and m. All will correspond to specific physics concepts and we will be able to collect data (in-class or virtually) for each of these concepts.
Page updated
Google Sites
Report abuse