Presentation on theme: "Kinematics in One Dimension"— Presentation transcript:
1 Kinematics in One Dimension Chapter 2Kinematics in One Dimension
2 Kinematics deals with the concepts that are needed to describe motion.Dynamics deals with the effect that forceshave on motion.Together, kinematics and dynamics formthe branch of physics known as Mechanics.
7 SI units for speed: meters per second (m/s) 2.2 Speed and VelocityAverage speed is the distance traveled divided by the timerequired to cover the distance.SI units for speed: meters per second (m/s)
8 Example 1 Distance Run by a Jogger 2.2 Speed and VelocityExample 1 Distance Run by a JoggerHow far does a jogger run in 1.5 hours (5400 s) if hisaverage speed is 2.22 m/s?
9 Average velocity is the displacement divided by the elapsed time. 2.2 Speed and VelocityAverage velocity is the displacement divided by the elapsedtime.
10 2.2 Speed and VelocityExample 2 The World’s Fastest Jet-Engine CarAndy Green in the car ThrustSSC set a world record of341.1 m/s in To establish such a record, the drivermakes two runs through the course, one in each direction,to nullify wind effects. From the data, determine the averagevelocity for each run.
16 2.3 AccelerationExample 3 Acceleration and DecreasingVelocity
17 2.4 Equations of Kinematics for Constant Acceleration
18 2.4 Equations of Kinematics for Constant Acceleration Five kinematic variables:1. displacement, x2. acceleration (constant), a3. final velocity (at time t), v4. initial velocity, vo5. elapsed time, t
19 2.4 Equations of Kinematics for Constant Acceleration
20 2.4 Equations of Kinematics for Constant Acceleration Example 6 Catapulting a JetFind its displacement.
21 2.4 Equations of Kinematics for Constant Acceleration
22 2.5 Applications of the Equations of Kinematics Reasoning Strategy1. Make a drawing.2. Decide which directions are to be called positive (+) andnegative (-).3. Write down the values that are given for any of the fivekinematic variables.4. Verify that the information contains values for at least threeof the five kinematic variables. Select the appropriate equation.5. When the motion is divided into segments, remember thatthe final velocity of one segment is the initial velocity for the next.6. Keep in mind that there may be two possible answers to akinematics problem.
23 2.5 Applications of the Equations of Kinematics Example 8 An Accelerating SpacecraftA spacecraft is traveling with a velocity of m/s. Suddenlythe retrorockets are fired, and the spacecraft begins to slow downwith an acceleration whose magnitude is 10.0 m/s2. What isthe velocity of the spacecraft when the displacement of the craftis +215 km, relative to the point where the retrorockets beganfiring?xavvotm-10.0 m/s2?+3250 m/s
24 2.5 Applications of the Equations of Kinematics xavvotm-10.0 m/s2?+3250 m/s
25 In the absence of air resistance, it is found that all bodies 2.6 Freely Falling BodiesIn the absence of air resistance, it is found that all bodiesat the same location above the Earth fall vertically withthe same acceleration.This idealized motion is called free-fall and the accelerationof a freely falling body is called the acceleration due togravity.
27 Example 10 A Falling Stone 2.6 Freely Falling BodiesExample 10 A Falling StoneA stone is dropped from the top of a tall building. After 3.00sof free fall, what is the displacement y of the stone?
28 2.6 Freely Falling Bodiesyavvot?-9.80 m/s20 m/s3.00 s
29 2.6 Freely Falling Bodiesyavvot?-9.80 m/s20 m/s3.00 s
30 Example 12 How High Does it Go? The referee tosses the coin up 2.6 Freely Falling BodiesExample 12 How High Does it Go?The referee tosses the coin upwith an initial speed of 5.00m/s.In the absence if air resistance,how high does the coin go aboveits point of release?
31 2.6 Freely Falling Bodiesyavvot?-9.80 m/s20 m/s+5.00 m/s
32 2.6 Freely Falling Bodiesyavvot?-9.80 m/s20 m/s+5.00 m/s
33 Conceptual Example 14 Acceleration Versus Velocity 2.6 Freely Falling BodiesConceptual Example 14 Acceleration Versus VelocityThere are three parts to the motion of the coin. On the wayup, the coin has a vector velocity that is directed upward andhas decreasing magnitude. At the top of its path, the coinmomentarily has zero velocity. On the way down, the coinhas downward-pointing velocity with an increasing magnitude.In the absence of air resistance, does the acceleration of thecoin, like the velocity, change from one part to another?
34 Conceptual Example 15 Taking Advantage of Symmetry 2.6 Freely Falling BodiesConceptual Example 15 Taking Advantage of SymmetryDoes the pellet in part b strike the ground beneath the cliffwith a smaller, greater, or the same speed as the pelletin part a?
35 Position-Time GraphsWe can use a position-time graph to illustrate the motion of an object.Position is on the y-axisTime is on the x-axis
36 Plotting a Distance-Time Graph AxisDistance (position) on y-axis (vertical)Time on x-axis (horizontal)Slope is the velocitySteeper slope = fasterNo slope (horizontal line) = staying still
37 Where and WhenWe can use a position time graph to tell us where an object is at any moment in time.Where was the car at 4 s?30 mHow long did it take the car to travel 20 m?3.2 s
40 Describing in Words Describe the motion of the object. When is the object moving in the positive direction?Negative direction.When is the object stopped?When is the object moving the fastest?The slowest?
41 Accelerated MotionIn a position/displacement time graph a straight line denotes constant velocity.In a position/displacement time graph a curved line denotes changing velocity (acceleration).The instantaneous velocity is a line tangent to the curve.
42 Accelerated MotionIn a velocity time graph a line with no slope means constant velocity and no acceleration.In a velocity time graph a sloping line means a changing velocity and the object is accelerating.
43 Velocity Velocity changes when an object… Speeds Up Slows Down Change direction
44 Velocity-Time Graphs Velocity is placed on the vertical or y-axis. Time is place on the horizontal or x-axis.We can interpret the motion of an object using a velocity-time graph.
45 Constant VelocityObjects with a constant velocity have no accelerationThis is graphed as a flat line on a velocity time graph.
46 Changing VelocityObjects with a changing velocity are undergoing acceleration.Acceleration is represented on a velocity time graph as a sloped line.
47 Positive and Negative Velocity The first set of graphs show an object traveling in a positive direction.The second set of graphs show an object traveling in a negative direction.
48 Speeding Up and Slowing Down The graphs on the left represent an object speeding up.The graphs on the right represent an object that is slowing down.
49 Two Stage RocketBetween which time does the rocket have the greatest acceleration?At which point does the velocity of the rocket change.
50 Displacement from a Velocity-Time Graph The shaded region under a velocity time graph represents the displacement of the object.The method used to find the area under a line on a velocity-time graph depends on whether the section bounded by the line and the axes is a rectangle, a triangle
51 2.7 Graphical Analysis of Velocity and Acceleration
52 2.7 Graphical Analysis of Velocity and Acceleration
53 2.7 Graphical Analysis of Velocity and Acceleration