one-dimensional motion
DESCRIPTION
One-Dimensional Motion. Introduction to Displacement and Velocity. Objectives. Define and calculate displacement Differentiate between displacement and distance Solve velocity problems Differentiate between velocity and speed. Displacement. - PowerPoint PPT PresentationTRANSCRIPT
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One-Dimensional Motion
Introduction to Displacement and Velocity
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Objectives
Define and calculate displacementDifferentiate between displacement and distanceSolve velocity problemsDifferentiate between velocity and speed
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DisplacementStraight-line distance between the initial and final points Has direction and magnitudeΔx, xf-xi
X represents positionCan be positive or negativeMeasured in ft, m, km, etc
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DistanceNot the same as displacementOnly has magnitude, no directionAlways greater than
or equal to displacement
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Examples
If I walk 2 m east, what is my displacement?If walk 2 m east and 2 m west, what is my displacement?Graph
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Vectors Vs Scalars
Vectors- Quantities that have magnitude and directionScalars-quantities that only have magnitudeResultant- vectors added together
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Velocity
Change of position of an object over an interval of timeV=Δx/Δt = xf-xi/t f-t I
Has magnitude and directionVector or scalar?
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Example
Ms. K takes her dog Zeus for a walk. If they walk for 27 min and travel 1.89 km east, what is their average velocity in meters/sec?
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Speed
The change in distance over an interval of timeSpeed=Δx/Δt= xf-xi/t f-t I
Only has magnitude no direction!Vector or scalar?They are the same only when moving in a straight line
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Example 1
Polar Bears are extremely good swimmers with an average speed of 2.6 m/s, how far will it have traveled after 2.0 minutes?
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Example 2
Ms. K and Zeus embark on a walk. If they leave Ms. K’s house, travel a distance of 1.2 km and return to the house in 12 minutes and 13 seconds, A) what was their average velocity?
B) What their average speed? Give your answer in m/s
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Example 3
Zeus and Ms. K embark on a southbound journey. First they walk south at 6.5 km/hr for 1.1 hours. Then they stop to take a nap for 18 minutes and then continue south at 5.5 km/hr for 1.2 hours. A) What was their average velocity? B) What was their displacement?
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Example 4- Honors
To qualify for the finals in a racing event a race car must achieve an average speed of 250 km/h on a track with a total length of 2000 m. If a particular car covers the first half of the track at an average speed of 230 km/hr, what minimum average speed must it have in the second half of the event to qualify?
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One-Dimensional Motion
Graphing Position as a function of time
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Objectives
Draw and interpret distance versus time graphsInterpret what the slope indicatesDifferentiate between average velocity and instantaneous velocity
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Distance Versus Time Graph
Distance
TimeWhat is slope? The symbol? What does the slope here indicate?????
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Example
Distance
Time What is the slope? What is the velocity?
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Example
Distance
Time What is the slope? What is the velocity?
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Example
Distance
Time What is the slope? What is the velocity?
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Example
Distance
Time What does this indicate about the velocity of the object at each part?
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Instantaneous Velocity
Instantaneous velocity-velocity at a specific point in timeExamples?Average Velocity-velocity over a time durationExample?
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Example
Distance
4m
2m 5 10 15 20 time (seconds)What is the velocity between 0-5 seconds?Instant or average?
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Example Cont
Distance
4m
2m 5 10 15 20 time (seconds)What is the velocity between 5-10 seconds?Instant or average?
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Example Cont
Distance
4m
2m 5 10 15 20 time (seconds)What is the velocity at 6 seconds? 9.8 seconds?Instant or average? What is the velocity for 0-20 seconds?
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One-Dimensional Motion
Acceleration
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Objectives
Define accelerationSolve acceleration problemsDraw and interpret velocity versus time and acceleration versus time graphs
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Acceleration
The rate that velocity changes, so the change in velocity over the change in timea= Δv/Δt = V f – V i / t f – t I
Units- m/s2
Vector or scalar?
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Example
A sprinter goes from 10 m/s to 15 m/s in 5 seconds, at what rate is the sprinter accelerating?
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Example
I am driving east at 9.0 m/s and I see a deer and stop in 5.0 seconds
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Instantaneous Versus Average
Average acceleration-change in velocity over an interval of timeInstantaneous Acceleration-change in velocity at an instant of time
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Example
A runner starts at a velocity of -1.2 m/s and speeds up constantly during a workout. After 25 minutes the treadmill has a velocity of -6.5 m/s. What is the average acceleration during this time?
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Velocity Versus Time Graph
Velocity
TimeSlope=rise over runWhat does slope indicate here?What about other types of graphs?
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Example
Velocity
TimeWhat does this tell us about the acceleration?
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Example Continued
Accel
time
Acceleration is __________ and is below the time axis because _________________
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Example Continued
What does the distance versus time graph look like?
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Example
Velocity
TimeDraw the acceleration vs time graph and the position vs time
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One-Dimensional Motion
Uniformly Accelerated Motion
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Objectives
Solve problems using uniform acceleration equations
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Uniformly Accelerated Motion
Acceleration is constantWhat would a velocity versus time graph look like with constant acceleration? Without constant? EquationsV f = V i + atΔx = V i Δt + ½ (a t2)Vf
2 = Vi2 + 2 a Δx
Δx = ½ (Vf – Vi) Δt What variables do we have?
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Example
How long must a runway be for a plane to reach a takeoff velocity of 75 m/s if it accelerates at 20 m/s2?
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Example
My tea tumbler falls off my car and slides along 95 South for 75 m. Friction slows my tumbler at 6 m/s2.A)How fast was the car moving when the tumbler fell?B)How long did it take the tumbler to stop?
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One-Dimensional Motion
Freefall
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Objectives
Define freefallSolve freefall problems
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Freefall
If the only force acting upon an object is gravity the object is said to be in freefallNo _________________Considered to be uniform accelerated motiong is the acceleration due to gravity= 9.8 m/s2
When an object is in freefall we will use -9/8 m/s2
Does mass matter?What would a distance versus time graph look like for a ball being thrown in the air?
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Example
A ball is dropped from a height of 2.0 m. What is the velocity before it strikes the ground? How long did it take to hit the ground?
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Example Cont
Draw the position, velocity, and acceleration graphs
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Example continued
How long would it take for the same ball to be thrown up 2m and then fall to the ground?
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Example
A ball is thrown straight down with a speed of 0.50 m/s from a height of 4.0 m. What is the speed of the ball 0.70 seconds after the ball is released?
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Example
A 0.25 kg baseball is thrown upward w/ a speed of 30 m/s. Neglect friction. What is the maximum height that the baseball reaches?