Lesson 8.1: Kinematics Key Points:
Graphs
• Understand what information can be read from Kinematics Graphs.
• Understand that Graphs and Equations from Kinematics show the same information in different ways.
• Learn that Kinematics equations are derived from graphing.
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Often in Physics we want to represent data visually, to do this we use graphs. Position Time Graphs
Position­Time graphs are used to represent the location of a moving object over the course of time (thus we can read displacement directly off these graphs). The diagram below is an example of a position time graph. Notice that when the graph is a straight line (not parallel to the x­axis) the object is travelling at a constant velocity. If the graph is a curve the object is undergoing acceleration (either positive or negative), and if the graph is a line (parallel to the x­axis) the object’s position is not changing i.e. it is standing still. 2
Slope Calculations
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Instantaneous velocity can be found from a curved position time graph. To do this we draw a tangent to the curve that touches the curve at the exact point where we wish to know the instantaneous velocity. 5
Velocity­Time Graphs
A velocity­time graph is a useful tool that can be used to describe motion with either constant or changing velocity. A plot of velocity vs. time and distance vs. time for the same data is shown in the figure below. In the velocity time graph each point has the same vertical value because the velocity is constant. The line is parallel to the x­axis. hp://www.cdli.ca/courses/phys2204/
unit01_org01_ilo01/b_activity.htmlGraphing animation
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Look at the graph below.
How would you describe the runner’s velocity? 7
Velocity Time Graphs
• The vertical value of any point is the instantaneous velocity at that time. During the first five seconds, the runner’s instantaneous velocity increases. For the next five seconds, he runs at a constant speed of 8m/s, and over the last three seconds, he slows to a stop.
• Thus the area under the line on a velocity‑time graph is equal to the displacement of the object from its original position to its position at time t. When velocity is constant displacement increases linearly with time. If you plot the displacement versus time, you will get a straight line with a slope equal to velocity. 8
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Using the position vs. time graph at right, calculate the a) total displacement b) total distance c) average velocity d) average speed of the object. +0.3m, 1.3m, +0.04m/s, 0.19m/s
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Using the position vs. time graph at right, calculate the a) distance travelled between 0 and 90s b) the displacement from 20s to 80s c) the speed over the whole trip d) the velocity over the whole trip. 600m, +100m, 8m/s, 0m/s.
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Using the displacement time graph at right, calculate the a) displacement from 0s to 4 s b) the total distance travelled c) the average speed over the whole trip, and the d) average velocity over the whole trip. ­4m, 14m, 2.3m/s, +1m/s.
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Using the velocity vs. time graph at right, calculate a) the acceleration between 12s and 14s b) the total displacement over the whole trip c) the average velocity over the whole trip d) the average acceleration between 14s and 20s and e) the average speed. ­4m/s2, ­12m,­0.6m/s, +1m/s2, 1.75m/s.
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Using the velocity vs. time graph at right calculate a) total displacement over the whole trip, b) average acceleration between 5s and 15s c) average speed over the whole trip. 0m, +1.6m/s2, 6m/s.
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Using the velocity vs. time graph at right, calculate a) the acceleration between A and B, b) the displacement between A and E, c) the acceleration between F and g, d) the average velocity between A and F, e) the total distance travelled. +10m/s2, 210m, 0m/s2, +27m/s, 315m.
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Using the velocity vs. time graph at right, calculate a) the acceleration between 7s and 9s, b) total displacement between 0s and 7 seconds, c) the average speed over the whole trip and d) the acceleration between 2s and 4s. ­1.5m/s2, +14.5m, 1.94m/s, +1m/s2.
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Using the position vs. time graph below, calculate the instantaneous velocity at a) 2s, b) 12s c)17s d) 20s. 3m/s, ­1m/s, ­2.5m/s, ­1.67m/s
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Using the position vs. time graph below, calculate a) average speed over the whole trip, b) average velocity between 300s and 500s, c) total displacement over the entire trip, d) distance travelled in the first 200s. 3m/s, ­3.75m/s, 0m, 750m.
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