3 Chapter 3: One Dimensional Motion
Link to Chapter 3 of the textbook
Section 3.1: Kinematics
Khan Academy: Displacement, Velocity, and Time Videos
Kinematics is the study of how things move. Distance is how far you have moved along the path you took, and is often given the symbol . Displacement is how far you moved from your initial position regardless of path (final minus initial position) and is calculated as:
where means the change in the -position, is the final position, and is the initial position. Both distance and displacement are measured in meters (m) when doing most calculations in physics (but always check for the units the question is expecting if it gives them!).
Recall that a scalar quantity is something that has magnitude only (how much you have) and is always a positive number (a negative indicates direction). A vector quantity has both magnitude and direction (how much and where it’s going) and can be positive or negative. Distance is a scalar, and displacement is a vector.
Section 3.2: Speed and Velocity
Khan Academy: Displacement, Velocity, and Time Videos
Speed is a scalar quantity indicating how fast something is moving, but does not include information on the direction (always positive). Speed is calculated as distance over time (how far you went divided by how long it took). Velocity is a vector including directional information, and is calculated as the displacement over time (the total distance you moved from your initial position divided by how long it took to arrive at the final position).
Average velocity is calculated as the displacement over a given time period in units of m/s.
Instantaneous velocity is the velocity at some particular instant in time. This is found by taking the limit of the average velocity as the time period goes to zero, which is the derivative of the expression for the position as a function of the time .
Section 3.3: Position vs. Time Graphs
Position vs. time, also called graphs, chart the position of an object on the vertical axis as a function of time on the horizontal axis. Caution: these are not maps of motion! Moving in the horizontal direction across the graphs is increasing in time, not position.
At every point on an graph, a line can be drawn tangent to the point (a straight line that just touches but does not intersect the curve at that point). The slope of this tangent line is equal to the velocity. Why is this? Consider taking the slope of this line by picking two random points on the line with coordinates and . Slope is calculated as rise (change in vertical position) over run (change in horizontal position), also written as , or (because our vertical axis is position and our horizontal axis is position), which we have defined as our average velocity.
What happens as we choose these points closer and closer together? The value of will approach zero, effectively taking the limit as we go to zero. Assuming the two points are right on top of each other ( = 0) we find the instantaneous