A position-time graph shows whether there is motion. The position of an object is on the y-axis and time is on the x-axis. [](https://docs.google.com/drawings/u/0/d/sAXhGRBt_6vE-GhJpLFxNxw/image?w=191&h=193&rev=1&ac=1&parent=1yAPuP9uJrLKqzLf2uXutXkkMDGTeO0G5cvr7W8rpUUE) The simplest position-time graph is a horizontal line as shown in figure 1. This means no change in position is being recorded. There is no motion. We call this “at rest.” The area under this curve has no meaning. ![[position time graph.png|Figure 2]] Another position-time graph shows a linear line headed up as shown in figure 2. This graph shows an object was recorded at position 1.5 meters from an origin then moved to 3 meters. This does not mean that the object went faster. Instead, it means the object moved at a constant velocity. Take the difference between the highest and lowest position and this is the displacement. [](https://docs.google.com/drawings/u/0/d/sHKUonAIXC93oM2LM1HjBoA/image?w=191&h=190&rev=1&ac=1&parent=1yAPuP9uJrLKqzLf2uXutXkkMDGTeO0G5cvr7W8rpUUE) Figure 3 is similar to figure 2 because it is also linear however there is a decrease in the position. This does not mean the object slowed down. This only means the object was moving toward the origin. The object is moving at a constant velocity. The displacement is found by taking the difference between the final and initial positions. The slope of the line is the velocity of the object. To find the slope, take the change in y and divide it by the change in time. [](https://docs.google.com/drawings/u/0/d/s2DCn-TH2-a_MJTAepZehaw/image?w=191&h=190&rev=1&ac=1&parent=1yAPuP9uJrLKqzLf2uXutXkkMDGTeO0G5cvr7W8rpUUE) Figure 4 is a curved line (J curve) and shows the speed increases over time. The line at the end of the graph is steeper than at the start of the graph. The slope of the line is steeper; meaning the change in position increases over time. [](https://docs.google.com/drawings/u/0/d/svBwMBet4KXy0dDy8fOrcJA/image?w=191&h=190&rev=1&ac=1&parent=1yAPuP9uJrLKqzLf2uXutXkkMDGTeO0G5cvr7W8rpUUE) Figure 5 is also a curve like Figure 4, but the speed is decreasing over time. The line at the end of the graph is less steep than at the start of the graph. The slope of the line is less steep; meaning the change in position decreases over time. Now we combine these types of graphs to get a better description of motion. [](https://docs.google.com/drawings/u/0/d/sgDheqGopDjU3vwKCdM2knQ/image?w=191&h=190&rev=1&ac=1&parent=1yAPuP9uJrLKqzLf2uXutXkkMDGTeO0G5cvr7W8rpUUE) Figure 6 combines two types of motion. The first part of the graph looks like figure 2. The second part looks like figure 1. The object moved the first 5 seconds at a constant velocity (the slope equals velocity) and then is at rest from 5 seconds to 9 seconds. The object moved from the origin to a position 2 meters. If we set a frame of reference that motion to the right is positive then we can state that the object moved to the right (positive) or left (negative) based on the slope. This means that the object moved to the right 2 meters in figure 6. This means we can now think about the meaning of a negative y axis. [](https://docs.google.com/drawings/u/0/d/sG3QwhqyxxWUEYwsUjIthiA/image?w=191&h=214&rev=1&ac=1&parent=1yAPuP9uJrLKqzLf2uXutXkkMDGTeO0G5cvr7W8rpUUE) Based on our frame of reference, we can state the object in figure 7 is moving to the left, reaches the zero point at 7 seconds, and approximately -1.5 meters around 9 seconds. The slope of the line will tell us the velocity. $v = \frac{0-3.5 m}{7s}$ = -0.5 $\frac{m}{s}$ The negative lets the reader know the direction of the motion. --- Return [[Home|Home]]