Position + Velocity + Acceleration - with Integrals

Welcome to Ready to Derive! In this video, we revisit position, velocity, and a little bit about acceleration, which we first learnt about in the unit on differentiation, but this time with the powerful tool of integration. We learn how to work from an acceleration or velocity function and find our way back to the position function. We recap distance versus displacement and modify to be able to find without knowing the position function. We learn to find the position of a particle given an earlier position in two ways. Most importantly, we learn how to do this all by hand and by using the TI-84.

   • Derivatives Applied: Projectile Motion  
   • Derivatives Applied: Particle Motion  

00:00 introduction
01:15 practice 1: potato launcher
05:00 displacement versus distance recap
08:13 displacement versus distance given v(t)
10:46 practice 2: displacement and distance
13:01 practice 2 b) without calculator
15:30 practice 3: finding position of particle, indefinite integral
19:11 practice 3 redone: finding position of particle, definite integral
21:25 summary of formulas
22:23 practice 4: displacement & average velocity
24:29 practice 4 continued: distance & position