One-Dimensional Motion
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Transcript of One-Dimensional Motion
One-Dimensional Motion
Introduction to Displacement and Velocity
Objectives
Define and calculate displacementDifferentiate between displacement and distanceSolve velocity problemsDifferentiate between velocity and speed
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
DistanceNot the same as displacementOnly has magnitude, no directionAlways greater than
or equal to displacement
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
Vectors Vs Scalars
Vectors- Quantities that have magnitude and directionScalars-quantities that only have magnitudeResultant- vectors added together
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?
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?
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
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?
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
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?
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?
One-Dimensional Motion
Graphing Position as a function of time
Objectives
Draw and interpret distance versus time graphsInterpret what the slope indicatesDifferentiate between average velocity and instantaneous velocity
Distance Versus Time Graph
Distance
TimeWhat is slope? The symbol? What does the slope here indicate?????
Example
Distance
Time What is the slope? What is the velocity?
Example
Distance
Time What is the slope? What is the velocity?
Example
Distance
Time What is the slope? What is the velocity?
Example
Distance
Time What does this indicate about the velocity of the object at each part?
Instantaneous Velocity
Instantaneous velocity-velocity at a specific point in timeExamples?Average Velocity-velocity over a time durationExample?
Example
Distance
4m
2m 5 10 15 20 time (seconds)What is the velocity between 0-5 seconds?Instant or average?
Example Cont
Distance
4m
2m 5 10 15 20 time (seconds)What is the velocity between 5-10 seconds?Instant or average?
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?
One-Dimensional Motion
Acceleration
Objectives
Define accelerationSolve acceleration problemsDraw and interpret velocity versus time and acceleration versus time graphs
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?
Example
A sprinter goes from 10 m/s to 15 m/s in 5 seconds, at what rate is the sprinter accelerating?
Example
I am driving east at 9.0 m/s and I see a deer and stop in 5.0 seconds
Instantaneous Versus Average
Average acceleration-change in velocity over an interval of timeInstantaneous Acceleration-change in velocity at an instant of time
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?
Velocity Versus Time Graph
Velocity
TimeSlope=rise over runWhat does slope indicate here?What about other types of graphs?
Example
Velocity
TimeWhat does this tell us about the acceleration?
Example Continued
Accel
time
Acceleration is __________ and is below the time axis because _________________
Example Continued
What does the distance versus time graph look like?
Example
Velocity
TimeDraw the acceleration vs time graph and the position vs time
One-Dimensional Motion
Uniformly Accelerated Motion
Objectives
Solve problems using uniform acceleration equations
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?
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?
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?
One-Dimensional Motion
Freefall
Objectives
Define freefallSolve freefall problems
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?
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?
Example Cont
Draw the position, velocity, and acceleration graphs
Example continued
How long would it take for the same ball to be thrown up 2m and then fall to the ground?
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?
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?