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displacement vs. distance traveled If a body with position function s (t) moves along a coordinate line without changing direction, we can calculate the total distance it travels from t = a to t = b.
AP Calculus Formula List Math by Mr. Mueller Page 2 of 6 [ ] ( ) ( ) ( ) Intermediate Value Theorem: If is continuous on , and is any number between and , then there is at least one number between and such that . f a b k f a f b c a b f c k= ... Displacement v t dt x a x b Total Distance v t dt = = = =
Possible discussion points: By integrating the acceleration equation, you can find the velocity equation and by integrating the velocity equation, you can find the displacement equation. Also, by find the area between the curve and the x-axis, you can find displacement and total distance.
Intermediate Value Theorem: If f is continuous on [a, b] and k is any number between f (a) and f ( b ), then there is at least one number c between a and b such that f ( c ) = k . 1
AP Calculus AB— Unit 6 Motion with Integrals: Position – Velocity – Acceleration – Speed – Total Distance – Displacement Page 6 Example 3 (numerical) The table gives the values for the velocity and acceleration of a particle moving along the x-axis for selected values of time t. Both velocity and
Differentiation Formulas d dx k = 0 (1) d dx [f(x)±g(x)] = f0(x)±g0(x) (2) d dx [k ·f(x)] = k ·f0(x) (3) d dx [f(x)g(x)] = f(x)g0(x)+g(x)f0(x) (4) d dx f(x) g(x ...
Displacement is the shortest distance between two positions and has a direction. Examples: The park is 5 kilometers north of here. Velocity refers to the speed and direction of an object. Examples: Object moving 5 m/s backwards. Acceleration is the rate of change of velocity per unit time.
