Motion: A Math Model Introduction Graphing Motion in 1 dimension

Motion in one dimension Now that you have Read/Studied/taken notes on one dimensional motion in terms of words, sketches and motion diagrams, and displayed them such as with dots on ticker tape as well as with vectors, we’ll now examine representing such information by means of graphs.

Displacement: Displacement: defined as the change in position of an object. Displacement vs time graphs are very important for describing and recording position and change in position. Position Vs Time Slope is the velocity

Velocity (constant) Velocity: defined as change in position or displacement divided by the change in the time over which the position changes. When the position change is constant, so is the velocity. Velocity Vs Time Constant Velocity Change in position is constant Area under the graph shows displacement Slope = velocity

Velocity (uniform acceleration) Velocity: defined as change in position or displacement divided by the change in the time over which the position changes. When the position change increases by a constant amount so does the velocity. Velocity Vs Time Velocity with uniform acceleration Slope = acceleration Area under graph is velocity

Velocity (non-uniform acc.) Velocity: defined as change in position or displacement divided by the change in the time over which the position changes. When the position change varies, so does the velocity. Velocity Vs Time Slope at a point is acceleration at that moment. While area under graph is the displacement.

Uniform Acceleration Acceleration: defined as the change in velocity divided by the time interval over which the change occurs. When the velocity changes by a constant amount there is uniform acceleration. Acceleration Vs Time Velocity increases by a constant amount. Area under the graph is the velocity.

Acceleration: defined as the change in velocity divided by the time interval over which the change occurs. When the velocity change varies there is not uniform acceleration. Acceleration Vs Time Velocity’s change is changing by a non-constant amount Area under graph is velocity