Presentation on theme: "Bellringer: 1/17 A runner is traveling 4.0m/s. Approximately, how fast is he traveling in miles per hour?"— Presentation transcript:
1Bellringer: 1/17A runner is traveling 4.0m/s. Approximately, how fast is he traveling in miles per hour?
2Chapter 2: Motion in One Dimension Section 1: Displacement & Velocity
3Motion – the change of an object’s position relative to some reference point The study of physical concepts such as mass and force is called dynamics.The dynamics of objects in motion is called kinematics.
4Scalar Vs. Vector Scalars Vectors Quantities described by a magnitude Quantities described by both a magnitude and direction
5Distance vs. Displacement Scalar, how much ground an object covered during its motionDisplacementVector, how far out of place an object is
6Displacement: ∆x = xf – xi Objects that are “at rest” are not in motion.An object undergoes displacement when its position changes.So, displacement is the change of position.The displacement measures how far an object has moved from it’s starting location.Note: ∆ is the Greek symbol “delta”. It means “a change in”.xf means final position.xi means initial position.Displacement: ∆x = xf – xi
7The displacement of an object does not always equal the distance it has traveled.
8Displacement can be either positive or negative…depending on your frame of reference. The right (or east) will be considered positive unless otherwise stated. Likewise with up (north).The left (or west) will be considered negative unless otherwise stated. Likewise with down (south).∆x = -4 cm∆x = 8 cmNegativePositive
9With your partner, discuss the following: What is this object’s position at 1 minute?What is the object’s position at 2 minutes?What is its displacement between 1 min and 5 min?Describe the motion of this object.
10Speed Vs. Velocity Speed Rate at which an object covers a distance Example: While on vacation, Lisa Carr traveled a total distance of 440 miles. Her trip took 8 hours. What was her average speed?
11Velocity: v = ∆x = (xf-xi) Average velocity – the total displacement divided by the total amount of time during the displacement.Velocity may be + or - , depending on the displacement.Velocity: v = ∆x = (xf-xi)∆t (tf – ti)
12Why refer to it as average velocity? Example:Suppose you traveled from your house to school…a distance of 4.0 km. It took you .20 hours (12 minutes) because of heavy traffic.Your avg velocity would be:v = 4.0 km / .20 hv = 20 km/hDid you travel at that exact speed for the entire trip?Of course not.Because of this, velocity is an average.
13Velocity and speed are not the same: Velocity requires direction.Speed refers to the numerical value of velocity.
14Avg. Speed and Avg. Velocity I walk 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. The entire motion lasted for 24 seconds. Determine the average speed and average velocity.Average speed: 0.50m/sDisplacement is 0 meters, average velocity is 0m/s
15ExampleA crow flies east in a straight line. It begins flying at 3:04s, and comes to a rest at 3:11s. It was flying at an average velocity of 1.5 m/s. How far did the crow move from its initial position (in meters)?
16(Final) Displacement: xf = v∆t + xi Using the velocity equation, we can derive another equation to find an object’s positionWith your partner…1) Use the base velocity equation to derive an equation to solve for the final displacement of an object.(Final) Displacement: xf = v∆t + xi
17The slope of the line corresponds to the velocity. Velocity can be determined using a position vs time graph.The slope of the line corresponds to the velocity.
18Position vs Time How could we describe the motion of these objects?
20ExampleSketch a position vs. time and a velocity vs. time graph for the following: Your mother walks five meters to the kitchen at a velocity of 2 m/s, pauses by the refrigerator for three seconds, then walks back with a plate full of potato salad at a velocity of 1 m/s.
21Chapter 2: Motion in One Dimension Section 2: Accelerated Motion
22Acceleration: a = ∆v/∆t = vf - vi Definition: acceleration – the change in velocity over time.An object accelerates when it changes its motion.This means:Speeding upSlowing downChanging directionAcceleration: a = ∆v/∆t = vf - vitf - ti
23Acceleration has the derived unit of m/s2. But…what does this unit actually mean?With your partner…Use the acceleration formula to show how the unit of m/s2 is obtained.Explain, in plain speak, what the unit m/s2 means.m 1s sx=_m_s x ss2m_s_s
24The sign tells the direction. The magnitude of acceleration tells how quickly the change is happening.The sign tells the direction.Acceleration with a “+” magnitude means the object is gaining velocity in the “+” direction.Acceleration with a “–” magnitude means the object is slowing down (or gaining velocity in the “–” direction.
25Objects that have a constant velocity have no acceleration. Centripetal acceleration – the constant change of direction of an object moving in circles.
26ExampleTurner’s treadmill runs with a velocity of -1.2m/s and speeds up at regular intervals during a half hour workout. After 25 min, the treadmill has a velocity of -6.5 m/s. What is the average acceleration of the treadmill during this period?
27ExampleA shuttle bus slows down with an average acceleration of -1.8m/s/s. How long does it take the bus to slow from 9.0m/s to a complete stop?
28Acceleration can be determined using a velocity vs time graph. Use the image below to:Calculate the average velocity of the car.Create a velocity vs time graph for the car.Calculate the avg. acceleration of the car.
29Velocity vs TimeThe slope of a velocity vs time graph represents acceleration.
30Using the base equation for acceleration, we can find other equations to find the velocity and/or displacement of moving objects that are changing their speed…With your partner:Using the base equation for acceleration, derive two newequations to solve for initial displacement and final velocity.
31Bellringer: 1/22 What does the red line represent? What is the acceleration at A? B? C?
32xtABCGraphing !1 – D MotionA … Starts at home (origin) and goes forward slowlyB … Not moving (position remains constant as time progresses)C … Turns around and goes in the other direction quickly, passing up home
33Graphing w/ Acceleration xGraphing w/ AccelerationCBtADA … Start from rest south of home; increase speed graduallyB … Pass home; gradually slow to a stop (still moving north)C … Turn around; gradually speed back up again heading southD … Continue heading south; gradually slow to a stop near the starting point
34Tangent Lines t On a position vs. time graph: SLOPE VELOCITY Positive xTangent LinestOn a position vs. time graph:SLOPEVELOCITYPositiveNegativeZeroSLOPESPEEDSteepFastGentleSlowFlatZero
35Increasing & Decreasing txIncreasingDecreasingOn a position vs. time graph:Increasing means moving forward (positive direction).Decreasing means moving backwards (negative direction).
36Average SpeedWhat is the AVERAGE speed of the bass boat depicted in the graph?
37Average SpeedAverage speed is taking the total distance traveled (0 to 125 meters), and dividing by the total time (1 to 9 seconds) it takes.Average Speed = 125 meters = 15.6 m/s8 seconds
38Instantaneous SpeedWhat is the instantaneous speed of the bass boat at t=7 seconds?
39Instantaneous SpeedInstantaneous speed is speed at any given point in time. At 7 seconds, the distance is 85 meters; therefore the IS isInstantaneous Speed = 85 meters = 12.1 m/s7 seconds
40Speed Graphs In what time period is the bass boat speeding up? In what time period is the bass boat slowing down?When is the speed NOT changing?
41Graphing SpeedSpeed is usually graphed using a line graph, and it depicts the distance and time.Time is the independent variable, and thus is ALWAYS on the x-axis.Distance is the dependent variable, and is ALWAYS on the y-axis.
42Acceleration and Velocity As velocity increases, so does accelerationAs velocity decreases, so does accelerationWhen direction changes, so does accelerationWhen there is a constant velocity, there is no acceleration
44The Kinematic Equations describe the mathematical relationships that exist between an object’s motion.DisplacementVelocityAccelerationTime
45vf + vi 2 x = t Note that: Displacement with Constant Acceleration: This equation does not require acceleration.vf + vi2x =t
46ExampleA racing car reaches a speed of 42 m/s. It then begins a uniform negative acceleration, using its parachute and braking system, and comes to rest 5.5 s later. Find the distance that the car travels during braking. (Hint: list your givens)
47ExampleA car accelerates uniformly from rest to a speed of 6.6m/s in 6.5s. Find the distance the car travels during this time.
48vf = vi + a∆t Note that: Velocity with Constant Acceleration: This equation does not require displacement.∆t = (tf – ti)vf = vi + a∆t
49xf = xi + vit + ½at2 Note that: “t” is actually “∆t”. Displacement with Constant Acceleration:Note that:“t” is actually “∆t”.However, ti is usually 0.The equation can be rewritten to find xi.xf = xi + vit + ½at2
50ExampleA plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8m/s/s for 15s before takeoff. What is its speed at takeoff? How long must the runway be for the plane to be able to take off?
51vf2 = vi2 + 2a∆x Note that: Velocity with Constant Acceleration: This equation does not require time.∆x = (xf – xi)vf2 = vi2 + 2a∆x
52ExampleA person pushing a stroller starts from rest, uniformly accelerating at a rate of 0.500m/s/s. What is the velocity of the stroller after it has traveled 4.75m?
53Equations for Constantly Accelerated Straight-Line Motion
54Bellringer 9/9 a=11.2 m/s/s and d = 79.8 A race car accelerates uniformly from 18.5m/s to 46.1 m/s in 2.47 seconds. Determine the acceleration of the car and the distance it traveled.a=11.2 m/s/s and d = 79.8
55Falling Objectsfree fall – downward acceleration while under the effect of gravity only.Gravity is a force that causes objects to accelerate downward.
56All objects free fall with an acceleration of g= -9.8 m/s2. gravity causes objects to speed up as they fall downward and slow as they travel upwardwe will usually neglect air resistance until FRICTION is covered in more detail.For objects that are falling, launched, or thrown, downward acceleration is the value of gravity.
57Graphing Free FallCurved line on a position vs time graph signifies an accelerated motion
58Free Fall Practice Problems Upton Chuck is riding the Giant Drop at Great America. If Upton free falls for 2.6 seconds, what will be his final velocity and how far will he fall?D – 33mVf = 25.5 m/s
59Free Fall Practice Problems A feather is dropped on the moon from a height of 1.40 meters. The acceleration of gravity on the moon is 1.67 m/s/s. Determine the time for the feather to fall to the surface of the moon.T=1.29s
60Practice ProblemsA race car traveling at 44 m/s accelerates to a velocity of 22 m/s over a period of 11 seconds.What was the car’s displacement during this time?360 m.
61Practice ProblemsA bike rider accelerates to a velocity of 7.5 m/s during 4.5 seconds.If the bike had a displacement of 19 m, what was its initial velocity?.9 m/s
62Bellringer 9/10A tennis ball is thrown vertically upward with an initial velocity of +8.0m/s. What will the ball’s speed be when it returns to its starting point? How long will the ball take to reach its starting point?
63Practice ProblemsA stone is dropped into a deep well and is heard to hit the water 3.41s after being dropped. Determine the depth of the well.-57.0
64Practice ProblemsSketch a position time graph for the following scenarios:An object moving with a constant positive velocityAn object at rest
65Practice ProblemsSketch a velocity time graph for the following motionsA city bus that is moving with a constant velocityA tiger that is speeding up at a uniform rate of acceleration while moving in the negative direction
66Practice ProblemsA train accelerates from a velocity of 21 m/s with an acceleration of 3 m/s2 over a distance of 535 meters.What is the final velocity of the train?60 m/s
67Practice ProblemsA worker drops a wrench from the top of a tower 80.0m tall. What is the velocity when the wrench strikes the ground?-39.6 m/s
68Practice ProblemsA car moving eastward along a straight road increases its speed uniformly from 16 m/s to 32 m/s in 10.0s.What is the car’s average acceleration?What is the car’s average velocity?How far did the car move while accelerating?