CHAPTER 2 Kinematics in One Dimension

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We begin our study of one-dimensional kinematics with a look at some concepts familiar to us all - distance and speed. In order to describe more complex motions we'll extend these basic concepts by adding direction to our descriptions. Distance and speed will lead us to displacement and velocity.

We'll also use this opportunity to point out some techniques that are essential to efficient problem-solving practice.

Instantaneous Velocity

So far we've just considered average velocity. But when we talk about velocity we are usually interested in a velocity at a given instant - "How fast are we going?" Here's a look at instantaneous velocity.

In summary... The slope of a chord between any two instants on an x,t graph equals the average velocity between those two instants. If the velocity is constant, the graph will be a straight line. The average velocity calculated between any two points on this line equals the constant velocity.

If the velocity is not constant, we have a problem since Δx/Δt is undefined at an instant, that is, when Δt = 0. But we know we can have a velocity at an instant. So the equation is just not up to the task. So along come Newton and Leibnitz and poof we have calculus which can handle this situation. We'll just take it on faith.

We also note that we can find the instantaneous velocity from an x,t graph from the slope of a tangent to the graph at that instant.