Speed how fast an object is moving (also, the magnitude of the velocity) scalar
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1 Mechanics Recall Mechanics Kinematics Dynamics Kinematics The description of motion without reference to forces. Terminology Distance total length of a journey scalar Time instant when an event occurs interval duration of an event Position location relative to a reference point vector Displacement change in position vector Velocity rate of change of position vector Speed how fast an object is moving (also, the magnitude of the velocity) scalar Acceleration rate of change of velocity vector
2 Position-Time Graphs A position-time graph shows how the position of an object varies with time. By examining a position-time graph we can determine many things about the motion of an object. These include: describing the motion of the object determining the position at a given time o by interpolation (reading the graph) determining the distance traveled determining the displacement for an interval of time o difference between ending position and starting position determining the velocity of the object at a given instant (instantaneous velocity) o slope of the graph at that instant (tangent line) determining the velocity of the object over a given time interval (average velocity) o slope of the chord joining the point on the graph at the start of the interval to the point on the graph at the end of the interval
3 Example 1 Use the position-time graph below to answer questions 1 to B 150 Position (m) A C D Time (s) 1. What is the total distance the object moved? 2. What is the object s net displacement?
4 3. What is the object s velocity at t = 30 s? 4. What is the average velocity of the object from t = 10 s to t = 45 s?
5 Velocity-Time Graphs A velocity-time graph shows how the velocity of an object varies with time. By examining a velocity-time graph we can determine many things about the motion of an object. These include: describing the motion of the object determine the displacement for an interval of time o area under the graph (area above axis is positive, below axis is negative) determining the velocity of the object at a given time o by interpolation determining the velocity of the object over a given time interval (average velocity) o total displacement (area) during the interval divided by the time interval determining the acceleration of the object at a given instant (instantaneous acceleration) o slope of the graph at that instant (tangent line) determining the acceleration of the object over a given time interval (average acceleration) o slope of the chord joining the point on the graph at the start of the interval to the point on the graph at the end of the interval
6 Example 2 Use the velocity-time graph below to answer questions 5 to Velocity (m/s) Time (s) 5. What is the net displacement of the object?
7 6. What is the average velocity of the object for the entire interval? 7. What is the object s acceleration at t = 10 s? 8. What is the average acceleration of the object from t = 10 s to t = 50 s? Homework Motion Graphs Worksheet
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9 Motion Graphs Worksheet 1. Find the velocity in each section of the following position-time graph. ( 2.5 m / s, 0, 10 m / s, 3.8 m / s, 0, 8.8 m / s ) 2. Using the graph below, determine the average velocity for these intervals: a. AB ( 15 km / h) b. AD ( 5.0 km / h ) c. BD ( 2.5 km / h ) 3. Using the graph below, determine the average velocity for each of the following sections. a. t = 0 s to t = 2 s ( 10 m / s ) b. t = 6 s to t = 12 s ( 5.8 m / s ) c. t = 6 s to t = 15.5 s (0)
10 4. The following graph is that of an object moving in a straight line. East is considered as the positive direction. a. Determine the position of the object after 7.0 s. ( 10 m ) b. The graph shows five distinct sections. Briefly, and in general terms, describe the motion of the object in each of these sections. c. Considering the whole journey, calculate the average velocity. ( 1.4 m / s ) d. Find the instantaneous velocity at t = 13 s. ( 8 m / s) e. Using an appropriate scale, draw a velocity-time graph from the position-time graph. 5. This graph below describes the motion of an object moving in a straight line. At the beginning it is going east. From the graph determine each of the following. a. the object s displacement in the first 3.0 s (200 m [E]) b. the object s displacement between t = 3.0 s and t = 5.0 s (0) c. the total displacement of the object in 14 s (0) d. the average velocity of the object from t = 0 to t = 8.0 s (17.5 m/s [E])
11 6. Use the following graph of the motion of a car to find the total displacement (north is positive). (150 m [N]) 7. The following graph illustrates the motion of two cars traveling due north. Assuming that both cars were at the same position at t = 0, answer the following questions. a. At what time do both cars have the same velocity? ( t = 0.68 h ) b. At t = 0.4 h, which car is ahead and by how much? ( 26 km ) c. At t = 1.0 h, what is the distance separating the two cars? ( 25 km) 8. From the following graph, determine the acceleration for each interval, using the slopes. ( 2.0 m / s 2, 0, 1.8 m / s 2, 0, 1.0 m / s 2 )
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