Calculus Based Physics Lectures : How To Find Slope And Area Of Graph
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Learn how to find the slope and area of graphs in calculus-based physics with this comprehensive lecture. Understand the significance of slope in position, velocity, and acceleration graphs, and discover how the area under the curve reveals key physical quantities like displacement and work. Perfect for students looking to master graph interpretation in physics!
We define the position function x(t), the velocity function v(t) = dx/dt, and the acceleration function a(t) = dv/dt. The velocity function is the time derivative of the position function while the acceleration function is the time derivative of the velocity function. A velocity interval comes from a definite integral of the acceleration function over time. A displacement interval comes from a definite integral of the velocity function over time.
The average velocity is the slope of the position function over a time interval. If we shrink the time interval to approach 0, the average velocity becomes the instantaneous velocity, or the instantaneous rate of change of the position function. This says that the secant line slope becomes the derivative, the slope of the tangent line to the curve.
Note that speed is the magnitude of the velocity. Distance is the total integral of the velocity, no matter if the displacement is positive or negative.
We show several examples of differentiation of integration of various functions. This is where the fundamental theorem of calculus, indefinite integrals, integration rules, etc. are involved.
We also show examples of kinematics and graphs of position time graphs (x vs. t graphs), velocity time graphs (v vs. t graphs), and acceleration time graphs (a vs. t graphs).
Chapters (Timestamps)
0:00 Introduction to slopes and areas
0:21 Calculus applied to physics
1:32 Intro to Calculus Based Physics
1:51 Secant Line Slope approaching Tangent Line Slope
6:18 Function, derivative, integral
17:31 Race car position vs. time, velocity vs. time, acceleration vs. time
24:45 x vs. t compared to motion diagram (strobe positions)
27:10 Graphical representations of kinematics motion variables
31:31 Summary
32:28 Take action! Like! Subscribe! Share!
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