This calculus video tutorial explains the concepts behind position, velocity, acceleration, distance, and displacement, It shows you how to calculate the velocity function using derivatives and limits plus it contains plenty of notes, equations / formulas, examples, and particle motion practice problems for you to master the concept.
Here is a list of topics:
1. The position function – S(t) – Calculating the total distance traveled and the net displacement of a particle using a number line.
2. Average velocity vs Instantaneous Velocity – Equations / Formulas
3. Slope of the secant line vs Slope of the tangent line
4. Average rate of change vs Instantaneous Rate of Change
5. How to tell if a particle is moving to the right, left, at rest, or changing direction using the velocity function v(t)
6. Average acceleration vs Instantaneous Acceleration
7. Acceleration is positive when velocity is increasing
8. Acceleration is negative when velocity is decreasing
9. Acceleration is zero at constant velocity or constant speed
10. Instantaneous Speed is the absolute value of velocity
11. Vectors – Magnitude & direction – displacement, velocity and acceleration
12. Scalar Quantities – Speed and Distance
13. Average Speed is total distance divide by change in time
14. Average velocity is displacement divided by time
15. Number line and interval notation
16. The particle is moving to the right when the velocity is positive
17. The particle is moving to the left when velocity is negative.
18. The particle is at rest or changing direction when velocity is zero.
19. How to calculate instantaneous speed and velocity
20. How estimate instantaneous velocity for data tables using average velocity
21. How to find the intervals when the particle is moving to the right, left, or is at rest
22. Intervals when velocity is increasing or decreasing
23. How to find the intervals when the particle is speeding up or slowing down using a sign chart of acceleration and velocity
24. Calculating distance and displacement from the position function s(t)
25. Interval Notation – Brackets vs Parentheses
26. Derivative of position is velocity
27. Derivative of velocity is acceleration
28. calculating the velocity function using the definition of the derivative equation or the limit process / difference quotient
29. Calculating the instantaneous rate of change / slope of the tangent line