3 Which car experiences the greatest acceleration?
4 Match a GraphConsider the position-time graphs below. Each one of the 3 lines on the position-time graph corresponds to the motion of one of the 3 cars. Match the appropriate line to the particular color of car.
14 Questions:Where does the graph have positive slope?What does this positive slope mean?Where does the graph have negative slope?What does this negative slope mean?Is there any place(s) on the graph where the object is not moving?How do you know?What is the slope of the graph at this section?
15 Average Speed vs Average Velocity Velocity is not the same as speed.average velocity- the change in position divided by the time it took for that change to occur; a ratio of an object’s change in position (displacement) to the time it takes for that change to occurvavg = distance traveledtime of travelvavg = ∆x∆t
16 Speed or Velocity? speed & velocity are different quantities speed is the rate distance covered over timespeed is a scalar quantityvelocity is the rate displacement traveled over timevelocity is a vector quantityspeed & velocity equal magnitudes when an object does not change direction
17 Average VelocityConsider a car moving with a constant velocity of +10 m/s for 5 seconds. The diagram below depicts such a motion.
18 Average VelocityThe position-time graph would look like the graph below:
19 How would this graph look? Average VelocityNow consider a car moving at a constant velocity of +5 m/s for 5 seconds, abruptly stopping, & then remaining at rest (v = 0 m/s) for 5 seconds.How would this graph look?
22 Instantaneous Speedspeed at any given point in time
23 Can I use one point to find velocity? Important Note: DO NOT use one point to calculate velocity on a position-time graph!!!bcade
24 Example 2—Drawing Graphs from Graphs Use the position vs time below to draw a velocity vs time graph.
25 Solution Velocity vs Time 6 5 4 3 2 1 -12 -8 -4 12 8 Velocity (m/s) 128Velocity (m/s)Time (s)
26 Position vs Time Graphs the x-t graph of a constantly moving object is linear
27 Position vs Time Graphs the slope of an x-t graph is rise (position) over run (time)for an x-t graph,m = ∆x∆t
28 Position vs Time Graphs the change in position of an object is displacement, ∆xthe rate change in position of an object over an interval of time (the time it takes for the change to occur) is called average velocity, vavgvavg = ∆x∆t
38 Velocity vs Time Graphs a velocity (v) vs time (t) graph plots velocity as a function of timethe v-t graph of a constantly moving object is a horizontal lineremember, horizontal lines have zero slope
39 Velocity vs Time Graphs the v-t graph of an object moving at a changing rate is a diagonal linethe velocity is changing by a constant rate
41 Constant, Uniform Acceleration Bessie took a trip on her bicycle. The data of Bessie’s bike ride below, along with its accompanying graph, is shown. Use the graph to answer the questions that follow:
42 Constant, Uniform Acceleration Questions:What do you notice about this position vs time graph?What does that mean?
43 Constant, Uniform Acceleration Now, here is the data, along with the resulting velocity vs time graph, of the same bike ride.
44 Constant, Uniform Acceleration Questions:What can you say about the slope of this graph?What does that mean?
45 Constant, Uniform Acceleration Conclusions:If an object has constant velocity, then that object has zero acceleration.Constant velocity Δv equals zero.The graph of zero acceleration is a horizontal line.All horizontal lines have zero slope because Δy equals zero.
47 Velocity vs Time Graphs the slope of a v-t graph describes changing velocity over timem = ∆v∆t
48 Velocity vs Time Graphs the rate at which velocity changes over an interval time is known as acceleration, aavgmathematically,aavg = ∆v∆t
49 Velocity vs Time Graphs the slope of a v-t graph describes the acceleration of the object in motionPositive Velocity Positive Acceleration
50 Velocity vs Time Graphs units of acceleration: m/s/s, m/s2acceleration is a vector quantityacceleration describes a change in velocity in the positive directionacceleration also describes a change in directiondeceleration (negative acceleration) describes a change in velocity in the opposite direction
85 Lines That IntersectSometimes, a problem will ask you to compare/contrast the motion of 2 objects.To do this, use the information provided in the problem to construct a position vs time graph.Then, use the graph to compare/contrast the 2 objects’ motions.
99 SolutionSince you are looking for the point where Harry & Sam pass each other, that means the coordinates (tH, xH) & (tS, xS) are equal.So, set the 2 equations for each line equal to each other & solve for t.
101 Solution xH = 10t = (10.0 m/s) (7.5 s) xH = 75 m Now, that you know at what time Harry catches up to Sam, you can calculate at what place this happens.Plug the value for time (7.5 sec) into the equation & solve for x.xH = 10t= (10.0 m/s) (7.5 s)xH = 75 m