Chapter 2 Kinematics in One Dimension - virt.wcskids.netvirt.wcskids.net/mmstc/staff_websites/mcmillan files/11 PHYSICS/(C2...Displacement vs time graph Constant Acceleration •Displacement

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 +/-

Direction 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

Rate of Change in Position

SPEED 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:

Mens 100 m world record

What is the average speed?

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

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?

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

Using Graphs to Solve Problems

A biker on a green road bike 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?

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 jumps 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