Chapter 2 Kinematics in One Dimension: Vector / Scaler Quantities … · 2020. 9. 21. · Chapter 2 Kinematics in One Dimension: • Vector / Scaler Quantities • Displacement, Velocity,

Chapter 2Kinematics in One Dimension:

• Vector / Scaler Quantities• Displacement, Velocity, Acceleration• Graphing Motion

• Distance vs Time Graphs• Velocity vs Time Graphs

• Solving Problems• Free Falling Objects

Chapter 2Kinematics in One Dimension:

Describing Motion:

Change in Position

Describing Motion:2 Types of Quantities

Vector Scaler

Magnitude and Direction

Example: ForcePush away from youPull Towards you

Described with arrows or +/-

Magnitude Only

Examples:MassTemperatureTime

Measuring Change in PositionDistance Displacement

Scaler QuantityTotal distance (total number of steps)

EXAMPLE:Track & Field4 x around the track =1600m (one mile)

Vector QuantityMeasured as Straight Line From Start to FinishCan be Positive or Negative

EXAMPLE:Track & Field4 x around Track = zero displacement

3m

4m

4m

3m

D C

BA

A-C?A-D?A-A?

1) What is the persons displacement in the first 20 seconds?

2) What distance did they travel in the first 20 seconds?

3) What is the maximum displacement from home?

4) What is the persons final displacement?

5) What is the total distance traveled?

Displacement Vs. Distance on Graph

Rate of Change in PositionSPEED VELOCITY

Rate of change in distanceScaler Quantity

𝑣 =𝑑

𝑡

m/s (meters /second)

Speedometer

Speed is Magnitude of Velocity

Rate of change in displacementVector Quantity

Ԧ𝑣 =𝑑

𝑡

m/s (meters /second)

Can be:positive negativeNorth southEast westRight leftUp down

Example:

What is the average speed?

How long will it take to run 1 mile (1600m)?

How far will he travel in 1 hour?

Example: Unofficial Record

What is the average speed?

How far will he travel in 1 hour?

Rate of Change of Velocity

Vector Quantity

𝑎 =Δ𝑣

Δ𝑡= 𝑣2−𝑣

1

𝑡2−𝑡

1

(m/s)/s = m/s2

Any change in velocity is acceleration

• Gaining or losing speed

• Changing Direction

Deceleration

Scaler Quantity

Losing Speed

Acceleration

Examples: A car accelerates from 0 m/s to 25 m/s in 2.9 seconds.What is the acceleration of the car?

A car moving at 15 m/s slows to 5.0 m/s in 3.0 seconds. What is the acceleration of the car?How long will it take to stop?

Chapter 2Kinematics in One Dimension:

• Vector / Scaler Quantities• Displacement, Velocity, Acceleration• Graphing Motion

• Distance vs Time Graphs• Velocity vs Time Graphs

• Solving Problems• Free Falling Objects

Speed Vs. Velocity on a Graph a) What average speed of the person from 0 to 10 seconds?

b) What average velocity of the person from 15 to 30 seconds?

c) What average velocity of the person from 40 to 55 seconds?

Graphing MotionDisplacement Time Graph

5 m 5 m5 m5 m 5 m

4m 4m 4m 4m

d

t

10m 10m 10m

Displacement Time Graph

Constant Velocity

Displacement is Directly related to time

Slope = Velocity (Δ𝑦

Δ𝑥=

Δ𝑑

Δ𝑡= 𝑣)

Y-intercept = starting position (di)

𝑦 = 𝑚𝑥 + 𝑏

𝒅 = 𝒗𝒕 + 𝒅i

D(m)

T(s)

4

10 15 20

8

5

12

Write equation to describe motion

An car starts from home and drives at 15m/s due north.A truck starts 250m north of the driver and drives 20 m/s to the south.

• Write an equation to describe the motion of the car.

• Write an equation to describe the motion of the truck.

• Sketch a graph of the car and trucks motion.

• When and where do they pass each other?

d

t

2m 8m6m4m 10m

d

t

3m12m 9m 6m

5m 3m4m 1m

Displacement vs time graphConstant Acceleration

• Displacement is exponentially related to time.

• Slope is always changing

• Parabolic Shape

• 𝑑 = 𝐴𝑡2+ 𝐵𝑡 + 𝐶

(+) acceleration

(-) acceleration

Velocity vs Time graph

5m/s 5m/s 5m/s 5m/s

2m/s4m/s6m/s8m/s

V (m/s)

T(s)

8m/s4m/s 12m/s 16m/s

Velocity Time GraphsConstant AccelerationVelocity is directly related to time.

• Slope = acceleration = Δ𝑦

Δ𝑥=

Δ𝑣

Δ𝑡= a

• y-intercept = initial velocity = vi

• 𝑦 = 𝑚𝑥 + 𝑏

• 𝑣 = 𝑎𝑡 + 𝑣i

Write equation that describes the motion in the graph above

A car moving at 20 m/s accelerates at 3.5m/s2 for 10s.

• Sketch a velocity time graph that represents the motion of the car

• Write an equation for the motion of the car.

• What is the final velocity of the car?

• When is the velocity 45 m/s?

V (m/s)

T(s)

Finding displacement using Velocity vs Time Graphs

A cat moves at constant speed of 4m/s for 10 seconds.How far does it travel?

A turkey starts from rest and accelerates to 6.0m/s om 10s.How far does it travel?

A duck moving at 4m/s accelerates to 10m/s in 10s..How far does it travel?

The AREA under a velocity vs. time graph is equal to displacement.

𝑑 =1

2𝑣1 + 𝑣2 𝑡 (Area of Trapezoid)

Finding displacement using Velocity vs Time Graphs

A bike rider moving at 8 m/s accelerates to 15 m/s over 8s.

• Sketch a velocity time graph that represents the motion of the rider

• What is the displacement of the rider?

• What is the acceleration of the rider?

V (m/s)

T(s)

Chapter 2Kinematics in One Dimension:

• Vector / Scaler Quantities• Displacement, Velocity, Acceleration• Graphing Motion

• Distance vs Time Graphs• Velocity vs Time Graphs

• Solving Problems• Free Falling Objects

Using Graphs to Solve Problems

The Green Jersey Rider is moving at 2.0m/s accelerates at 5m/s2

for 5 seconds.

• Sketch a d/t and v/t graph of the bikers motion.

• How far does the biker travel?

A purple people eater moving at 3m/s accelerates at 5m/s2 for a distance of 15.

• Sketch a d/t and v/t graph of the monsters motion.

• What is the final velocity of the monster?

Using Graphs to Solve Problems

Using Graphs to Solve ProblemsProblem Solving Hints• Draw picture or graph.

• List all Terms

• Determine which equations(s) to use

• Solve equation

• Plug in Terms

EXAMPLE: A runner moving at 3m/s accelerates at 4 m/s2 for 5 seconds.

• How far does the runner travel?

• What is the final speed of the runner?

Using Graphs to Solve ProblemsProblem Solving Hints• Draw picture or graph.

• List all Terms

• Determine which equations(s) to use

• Solve equation

• Plug in Terms

EXAMPLE: A kitten moving at 5m/s slides across the floor and comes to rest after 10m

• What was the acceleration of the kitten?

• How much time did it take to come to rest?

Chapter 2Kinematics in One Dimension:

• Vector / Scaler Quantities• Displacement, Velocity, Acceleration• Graphing Motion

• Distance vs Time Graphs• Velocity vs Time Graphs

• Solving Problems• Free Falling Objects

FREE FALLING OBJECTS

Acceleration due to gravity

Constant for all objects

a =g =9.8 m/s2

downward

Can be positive or negative depending on reference frame

32 ft/s2

FREE FALLING OBJECTS

EXAMPLE: A baseball is thrown straight up with a speed of 15 m/s.

• How high will it rise?• Vi = ?

• Vf at max height= ?

• a =

• How long will it be in the air?• Time up = ?

• Time down =?

FREE FALLING OBJECTS

A dude falls from the top of a cliff 10 m high.

• How long is he in the air?• Is there a change in direction?

• Vi = ?

• D = ?

• a =

• What is his final speed?• Vi = ?

• D = ?

• a =

FREE FALLING OBJECTS

A rock thrown upwards with velocity of 15 m/s from the top of a building 20 m high.

• How long is it in the air?• Is there a change in direction?• Vi = ?• D = ?• a =

• What is its final speed?• Vi = ?• a =• Vf =

World highest jump• What is the Velocity after 30

seconds?

• How far do they fall?

Felix Baumgartner Red Bull Stratos 2012

Chapter Summary

• Vector vs. Scaler

• Displacement, Velocity, Acceleration

• Graphing Motion• Displacement Graph

• Slope

• Equations

• Velocity Graphs• Slope, Area

• Equations

Problems Solving• Draw, list, choose, solve

Free Falling Objects• Acceleration of• Velocity / Acceleration at

Max height• Graphing