Have you ever wondered what the difference is between distance and displacement?
Look no further!
Distance is the amount traveled, regardless of any change in direction along the way, while displacement is just the amount span or interval between the starting point and ending point.
The Physics Classroom rightly compares these two ideas by stating that distance is a scalar or length, that refers to how much ground an object has covered during its motion, while displacement is a vector with length and direction, and refers to an object’s overall change in position.
Total Change Theorem
Simple enough, right?
But you know what is so confusing for students? Sometimes textbooks and professors use different terminology in expressing length and motion!
In some instances, the word distance will be used to describe displacement, and the phrase total distance will be used in place of the word distance.
So how will we know the difference?
There are some easy tricks for figuring out what a question is talking about, and this video will clear up any confusion.
In physics and calculus courses alike, the concept of distance and displacement, and how it relates to acceleration, velocity, and position is called the study of particle motion, and utilizes the definite integral.
We will draw upon our previous knowledge of how to find critical numbers to determine when a particle is at rest and if/when it changes direction.
Then we will learn how to write definite integrals given an initial condition and a derivative expression, and use the integral expression to find both distance and displacement.
Finally, we will look at a Free Response Question where we will use most of our derivative and integral techniques, as this question will ask us to find the:
- instantaneous rate of change
- average rate of change
- increasing and decreasing intervals
- definite integral expression for displacement
- average value function
- total distance
Particle Motion Video
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