Motion in One Dimension
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1 Motion in One Dimension Chapter 2 Physics
2 Table of Contents Position and Displacement Velocity Acceleration Motion with Constant Acceleration Falling Objects
3 The Big Idea Displacement is a change of position in a certain direction, not the total distance traveled
4 One-Dimensional Motion The simplest kind of motion Things can move forward and backward, but not left and right
5 Motion Takes place over time Depends upon the frame of reference What is frame of reference? Why do we choose one? How do we choose one? Once we decide upon a frame of reference, it remains fixed for the problem
6 Displacement When things start moving, the length of a straight line drawn from the object s initial position to it s final position is it s displacement In one dimension x = x x f i Change in position along x-axis = (final position on x-axis) (initial position on x-axis) Read the TIP at the bottom of p.41!
7 Motion in One Dimension Same concepts apply to any axis! Space shuttles instead of trains y = y y f i Change in position along y-axis = (final position on y-axis) (initial position on y-axis)
8 Equations for Chapter 2 x = x x f i v avg a avg = = x t v t v avg = v i x = ( vi + v f ) t 2 v f = v i v f + a t
9 More Equations 1 x = vi t + a( t 2 2 )
10 Keep in mind Displacement is not always equal to the distance traveled! Displacement can be positive or negative!
11 POSITIVE AND NEGATIVE QUANTITIES ARE JUST DIRECTIONS IN MOTION PROBLEMS!
12 Velocity Physics lets us figure out exactly what is happening in situations like this one.
13 Average Velocity Average velocity is the total displacement divided by the time interval during which the displacement occurred. v avg average velocity = x == ttt xx fi fi change in position change in time = displacement time interval
14 Velocity and Speed Velocity describes motion with both a direction and a numerical value (a magnitude). Speed has no direction, only magnitude. Average speed is equal to the total distance traveled divided by the time interval.
15 Velocity and Speed average velocity = change in position change in time = displacement time interval distance traveled average speed = time of travel
16 + s and s are Directional! Click here for a helpful animation
17 Practice Time Practice A 1-10 Teacher Demonstration #1 Working Together #2-#3 Guided Practice #4-#10
18 Interpreting Velocity Graphically For any position-time graph, we can determine the average velocity by drawing a straight line between any two points on the graph. If the velocity is constant, the graph of position versus time is a straight line. The slope indicates the velocity. Object 1: positive slope = positive velocity Object 2: zero slope= zero velocity Object 3: negative slope = negative velocity Click on Graph for Flash Animation
19 Instantaneous Velocity The instantaneous velocity is the velocity of an object at some instant or at a specific point in the object s path. The instantaneous velocity at a given time can be determined by measuring the slope of the line that is tangent to that point on the position-versus-time graph.
20 Instantaneous Velocity Movie Clip Can you graph the velocity for this bungee jumper?
21 Practice Time Section Review p.47 Homework for the weekend Due Monday P.68 2,4,5,6,10,11
22 Quick! You re in your car, driving at 100 km/h Situation 1: see a red light a quarter-mile away, so you slow down to a stop Situation 2: a deer runs out in front of you, so you slam on your brakes to stop In which situation do you feel the most?
23 Acceleration is rate of change of velocity with respect to time How much does your velocity change, and how fast does this happen?
24 Dimensions of a Work it out from the formula a is measured in m/s 2
25 Practice Problems 1. With an average acceleration of -1.2 m/s 2, how long will it take a cyclist to bring a bicycle with an initial speed of 6.5 m/s to a complete stop? A: 5.4 s 2. Suppose a treadmill has an average acceleration of m/s 2. a. How much does its speed change after 5.0 min? b. If the treadmill s initial speed is 1.7 m/s, what will its final speed be? 1.4 m/s and 3.1 m/s
26 Just like Velocity Acceleration is a vector quantity Has both a magnitude (speed) AND direction Can be positive or negative JUST DIRECTIONAL!!!
27 Graphs can tell us things
28 Small Group Questions If a baseball has zero velocity at some instant, is the acceleration of the baseball necessarily zero at that instant? If a passenger train is traveling on a straight track with a negative velocity and a positive acceleration, is it speeding up or slowing down? When you are out for a bike ride, you slow down on your bike as you approach a group of hikers on a trail. Explain how your acceleration can be positive even though your speed is decreasing.
29 Relating the two
30 Review Position: where are you at? Displacement: change in position Velocity: rate of change in position Acceleration: rate of change of velocity
31 Review
32 Motion with constant acceleration Velocity changes at a constant rate What does displacement really depend on? Acceleration Initial Velocity Time
33 Velocity vs. Time
34 Δx with constant a 1 x = ( v + v ) 2 i f t Let s see what we can do with this formula
35 p.53 Practice #1: 21 m #2: 18.8 m #3: 9.1 s #4: 24 m/s
36 Our lonely equation 1 x = ( v + v ) 2 i f t This is great, but what if we don t know v f? Can we still solve for displacement?
37 v with constant a v a = t = v f t v Rearranging the equation tells us that v f = v i + a t i
38 Finding displacement 1 x = ( vi + v f ) t 2 1 x = ( v + v + a t) 2 i i Let s substitute our new equation in for v f t 1 x = v t + a ( i 2 and simplify the new equation. t ) 2
39 p.55 Practice D m/s; 29 m m/s; 59.0 m m/s; 19 m s; 32 m
40 One last equation v 2 f = See handout: v 2 Final Velocity after any Displacement Equation Sheet Handout i + 2a( x) This is what you will get for your test next week 2
41 p. 58 Practice m/s 2. a. +21 m/s b. +16 m/s c. +13 m/s m/s m/s m 3. a. 16 m/s b. 7.0 s
42 Definitions Frame of reference: a system for specifying the precise location of objects in space and time Back
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