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“Number

Now that we’ve introduced the notion of an object following a straight path in water, it’s time for a formal discussion of motion on a line. One-dimensional kinematics helps us understand the motion of an object following a straight line with an origin point. Of importance is the straight line; we cannot have the object making "turns" or going about curves. Once the origin has been designated, we say that the object is at a negative position from the point if it’s to the left of the point, and a positive position if it’s to the right of the point.

Now that we’ve got our number line situated, it’s also important to consider the object as it moves in time. We typically represent the time with the variable 't' in seconds. When t = 0, the object may be anywhere on the number line; however, as ‘t’ increases (note 't' can't be negative), we track both the time and the displacement from our origin point. Hence, this creates two variables: time and position. Now, let’s take a look at how the two representations work together to capture the same motion!

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As you can see from above, because we have a graph with two variables, we can define a position function, d(t), which gives us the displacement from the origin at any point in time. Examples of position functions might include d(t) = 3t, or d(t) = cos(t). Hence, it is clear that there are two distinct ways to represent the object’s motion. All the while, it is much easier to look at a graph of time versus position, rather than watch an object move along a line in real-time, so we typically look at the particle’s position function. This will allow us to use the tools of calculus to learn about velocity and acceleration!


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