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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.
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.
By the Fundamental Theorem of Calculus, since. v t x ' t , the integral will yield . This is also known as displacement. The . answer can be positive or negative depending on if the particle lands to the . the . of its original . position. t 2. 6. v t dt. t 1. is another example of a or to .
To determine the displacement of an object, you only have to consider the change in position between the starting point and the ending point. The path followed from one point to the other does not matter.
If f is differentiable on I , except possibly at c , then f ( c ) can be classified as follows. ) 1 ( If f ' ( x ) changes from negative to positive at c , then f ( c ) is a relative minimum of f . ( 2 ) If f ' ( x ) changes from positive to negative at c , then f ( c ) is a relative maximum of f .
An easy to understand step-by-step method for applying integrals to determine the distance or the displacement based on a given application problem.
Define position, displacement, and distance traveled. Calculate the total displacement given the position as a function of time. Determine the total distance traveled.
