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?