G9 asp. 2.3 position time graph
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The velocity vector for an object in uniform circular motion is tangential to the circle. The velocity vector is always tangent to the circular path. It is changing direction but constant in magnitude. It is never directed toward or away from the center. The radius of the circle does not affect the velocity. The answer is A.
G9 asp. 2.3 position time graph
- 1. TOPIC 2.3 – POSITION- TIME GRAPHS FOR CONSTANT ACCELERATION GRADE 9 PHYSICS
- 4. Position-Time Graphs for Constant Acceleration The Position-time graph for a uniformly accelerated object is a parabola. The greater the curvature of the parabola, the greater the magnitude of the acceleration © 2014 Pearson Education, Inc.
- 5. Position-Time Graphs for Constant Acceleration Constant acceleration produces a parabolic position-time graph. The sign of the acceleration determines whether the parabola has an upward or downward curvature. © 2014 Pearson Education, Inc.
- 6. Position-Time Graphs for Constant Acceleration The magnitude of the acceleration is related to how sharply a position-time graph curves. In general, the greater the curvature of the parabola, the greater the magnitude of the acceleration. © 2014 Pearson Education, Inc.
- 7. Position-Time Graphs for Constant Acceleration Each term in the equation has graphical meaning. The vertical intercept is equal to the initial position xi. The initial slope is equal to the initial velocity. The sharpness of the curvature indicates the magnitude of the acceleration.
- 8. Position-Time Graphs for Constant Acceleration Thus, considerable information can be obtained from a position-time graph. © 2014 Pearson Education, Inc.
- 9. Position-Time Graphs for Constant Acceleration A single parabola in a position-time graph can show both deceleration and acceleration. A constant curvature indicates a constant acceleration. A ball thrown upward is an example of motion with constant acceleration. © 2014 Pearson Education, Inc.
- 10. V-t graph and d-t graph
- 11. V-t graph and d-t graph
- 12. V-t graph and d-t graph
- 13. V-t graph and d-t graph
- 14. V-t graph and d-t graph a-t AFL https://phet.colorado.edu/sims/cheerpj/moving-man/latest/moving-man.html?simulation=moving-man
- 15. Velocity – Time Graph describe motion by vt – graph velocity-time graph could have different shapes, three of them are: Time (s) velocity (m/s) Time (s) velocity (m/s) Time (s) velocity (m/s) Acceleration is obtained from velocity-time graph by calculating the slope: 𝑎 = 𝑠𝑙𝑜𝑝𝑒 = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = Δ𝑣 Δ𝑡 Displacement is obtained from velocity-time graph by calculating the area under graph: ∆𝑥 = 𝑎𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑔𝑟𝑎𝑝ℎ
- 16. Velocity – Time Graph Remember: When velocity line above x – axis its positive velocity. When velocity line below x – axis its negative velocity. Speeding up: a and v same dir. Slowing down: a and v opposite dir. positive velocity negative velocity positive acceleration negative acceleration no acceleration describe motion by vt – graph
- 17. Positive and negative constant velocity
- 18. Positive and negative velocities
- 19. Speeding up and slowing down
- 20. Positive and negative acceleration
- 21. Velocity – Time Graph describe motion by vt – graph Describe the motion for the figure beside: EX The object is speeding up with constant acceleration. The acceleration is positive and the velocity is positive. The opposite graph represents the motion of two objects A and B. Which of the two objects have more acceleration. Explain why. EX Object B has more acceleration. because the slope of its line is steeper (has more slope). AFL
- 22. Velocity – Time Graph describe motion by vt – graph Describe the motion for the figure beside: EX The object is slowing down (retarding) with constant acceleration. The acceleration is negative but the velocity is positive. The opposite graph represents the motion of two objects A and B. Which of the two objects have more acceleration. Explain why. EX Object B has more acceleration. because the slope of its line is steeper (has more slope). AFL
- 23. Velocity – Time Graph describe motion by vt – graph Describe the motion for the figure beside: EX moving with constant positive velocity, acceleration = 0 or slope = 0 Don’t confuse between velocity – time graph and position – time graph!!! slope = a slope = v AFL
- 24. Velocity – Time Graph obtain the acceleration from vt – graph The opposite graph represents the motion of running horse. a- Find the acceleration of the horse. Is the horse speeding up or slowing down? Justify your answer. EX 2 0 4 6 8 10 12 Velocity (m/s) Rise Run 𝑎 = 𝑠𝑙𝑜𝑝𝑒 = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = Δ𝑣 Δ𝑡 = 10 − 2 5 − 1 = + 2 𝑚/𝑠2 the acceleration (slope) is positive and velocity is positive ⇒ they are in the same direction. ⇒ The horse is speeding up ∆𝑥 = 𝑎𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑔𝑟𝑎𝑝ℎ = 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 b- find the displacement travelled by the horse after 5 seconds. = 1 2 × 𝑏𝑎𝑠𝑒 × ℎ𝑒𝑖𝑔ℎ𝑡 = 1 2 × 5 × 10 = 25 𝑚. AFL
- 25. Velocity – Time Graph obtain the acceleration from vt – graph The opposite graph represents the motion of running horse. Find the acceleration of the horse. Is the horse speeding up or slowing down? Justify your answer. EX 𝑎 = 𝑠𝑙𝑜𝑝𝑒 = 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = Δ𝑣 Δ𝑡 = 80 − 40 2 −6 = ‒ 10 𝑚/𝑠2 Velocity (m/s) Run Rise the acceleration (slope) is negative and velocity is positive. ⇒ they are in the opposite direction. ⇒ The plane is slowing down ∆𝑥 = 𝑎𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑔𝑟𝑎𝑝ℎ = 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒 + 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑟𝑒𝑐𝑡𝑎𝑛𝑔𝑙𝑒 b- find the displacement travelled by the horse after 6 seconds. = 1 2 × 𝑏𝑎𝑠𝑒 × ℎ𝑒𝑖𝑔ℎ𝑡 + 𝑙𝑒𝑛𝑔𝑡ℎ × 𝑤𝑖𝑑𝑡ℎ = 1 2 × 6 × (100 − 40) + 6 × 40 = 420 𝑚. AFL
- 26. Motion graphs
- 27. Motion graphs The opposite graph represents the motion of an object, describe the motion of this object. Use the simulation of the Moving man to obtain some experimental graphs of motion. Xi vi(m/s) a (m/s2) 0 0 3 0 12 -3 5 0 3 0 -12 3 0 -12 -3 -5 0 -3 AFL
- 28. Guided example
- 29. CW Centripetal acceleration always points to the of the circle. A. back B. center C. front D. outer edge
- 30. CW
- 31. CW
- 32. Assessment
- 33. Assessment 9. The velocity vector for an object in uniform circular motion is . A. tangential to the circle B. directed toward the center of the circle C. directed away from the center of the circle D. proportional to the radius of the circle