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Calculus Based Physics Slope and Area

Calculus based physics connects slope and area to derivatives and integrals of kinematics variables with respect to time. 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 definate integral of the acceleration function over time. A displacement interval comes from a definate 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, indefinate 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! --------------------- Please support us on Patreon: https://www.patreon.com/highpeakeduca... Please follow us on Facebook:   / high-peak-education-110762917338673   Please follow us on Twitter:   / highpeakeducate   Please follow us on Instagram:   / highpeakeducation   Please follow us on Reddit:   / highpeakeducation   Please follow us on TikTok:   / highpeakeducation   Interact with us on Twitch:   / highpeakeducation   Interact with us on Discord:   / discord   #HighPeakEducation #Calculus #Kinematics