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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