advertisement

1.4 Converting Graphs Types of Motion: Displacement & Velocity Graphs Slope of displacement-time graph give velocity Area of velocity-time graph gives the displacement Displacement & Velocity Graphs Slope of velocity-time graph give acceleration Area of acceleration-time graph gives the velocity [S] 1.4 Comparing Graphs → v-t Graph: Converting Graphs [S] Example #7: Use the graph above to answer the following questions. a) What is the velocity at t =3.0 s? Answer At 3.0 s, the velocity is 6 m/s [S] → V-T Graphs v-t Graph: [S] Example #7: b) What is the average velocity from 0s to 10s? = 1 1 = ℎ + = 4 8 /[] + 68/[] 2 2 = 16 + 48 = 64 [] = 64 [] = 6.4 [} 10 Average velocity is 6.4 m/s [S] Converting Graphs [S] Example #7: c) Make a position-time from 0s to 10s. Obtain the displacements by calculating the area. Determine the position by adding areas → v-t Graph: Converting Graphs v-t Graph: Time (s) Displacement(area) [S] Position m[S] Sum displscement 0 0 0 1 Displacement between 0 to 1s = 0.5 x 1sx1m/s =1 m 1 2 0.5 x(2m/s +4m/s)1s =3m 1+3 = 4 3 0.5 x (4m/s + 6m/s)1s =5m 9 =4 + 5 4 0.5 x (6m/s + 8 m/s) 1s =7 m 16 5 Displacement from 4s to 5s =1s x 8m/s= 8m 24 6 1 s x 8 m/s =8 m 32 7 1 s x 8 m/s =8 m 40 8 1 s x 8 m/s =8 m 48 9 1 s x 8 m/s =8 m 56 10 1 s x 8 m/s =8 m 64 [S] The area for the displacement between 1s to 2s is a trapezoid. The area is easily calculated using ½(sum of parallel sides)x Comparing Graphs Example #7 Soln: c) Time (in s) Position (in m [E]) 0 0 1 1 2 4 3 9 4 16 5 24 6 32 7 40 8 48 9 56 10 64 1.4 Comparing Graphs Example #7 Soln: 0 0 1 1 2 4 3 9 4 16 5 24 6 32 7 40 8 48 9 56 10 64 70 60 50 Position (m [S]) c) Time Position (in s) (in m [S]) Position-time graph 40 30 20 10 0 0 2 4 6 8 10 time (s) The position-time graph curves smoothly upwards from 0 s to 4s as the objects accelerates uniformly from 0 to 8m/s. From 4 s to 10 s the graph is a straight line sloping upwards as the object travels with uniform velocity of 8 m/s [S]. 12 1.4 Comparing Graphs d) Calculate the acceleration and draw an acceleration-time graph The acceleration is constant from 0s to 4s which is the slope. Slope = rise/run = = 8 −0 4−0 From 4s to 10 s = = 2.0 2 8 −8/[] 10 −4 = 0 m/ 2 1.4 Comparing Graphs Time acceleration (in s) m/s2 [S]) 2 1 2 2 2 3 2 4 2 4 0 5 0 6 0 7 0 8 0 9 0 10 0 2,5 2 Acceleration(m/s2 [S]) 0 Acceleration-time Graph 1,5 1 0,5 0 0 2 4 6 8 10 Time (s) Note the acceleration instantaneously change from 2 m/s2 to 0 m/s2 at 4s. This is shown by having two values at t=4 s. 12 1.4 Comparing Graphs What is the motion in each section of the following graph? → v-t Graph: B [W] C A D 1.4 Comparing Graphs What is the motion in each section of the following graph? → v-t Graph: B [W] A C D 1.4 Comparing Graphs What is the motion in each section of the following graph? → v-t Graph: A B C D 1.4 Comparing Graphs 1.4 Practice Questions: Page 34 Practice Q1 Page 35 Practice Q1-4 Finish Graph Worksheet