Science 10Aim: Calculating Conversions, Displacement, Time, speed and velocity

AgendaConversion examplesConversion worksheetLunch – extra help timeDisplacement and velocity notesHomework: read p. 137-154 (acceleration and velocity))

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Calculating Displacement Displacement: Example: Δd = d2 – d1

d1 = initial positiond2 = final position

Δd = 166 km 20o South of West

OR Δd = 166 km 20o

[W20o S]

Calculating Total Distance TraveledBecause distance is scalar (no direction), simply add together all the distance

Example:A student ran 50m east, 20m south, 35m west, and 25m north.

The total distance traveled is 230m.

Vectors = magnitude and DIRECTION Therefore, to indicate direction in equations we use negative and positive numbers

Direction conventions in Physics: Right is Positive (+) Left is Negative

(-)

East is Positive (+) West is Negative (-)

North is Positive (+)South is Negative (-)

Up is Positive (+) Down is Negative (-)

Calculating Total DisplacementTotal displacement of one object moving

several different displacements is the vector sum of the displacements.

Δdtotal = d1 + d2 + …

Example: A student walks 23m N, turns around and walks 33m S. What is the

student’s total displacement?

Calculating Total DisplacementTotal displacement of one object moving several different displacements is the vector sum of the

displacements.

Δdtotal = d1 + d2 + …

Example: A student walks 23m N, turns around and walks 33m S. What is the student’s total

displacement?

Δdtotal = d1 + d2 + … = (+23m) + (-33m)

= - 10m (or 10m S)

Time (t)is a point in time as it relates to your reference or zero time.

A time interval (t) is the difference between two times.

t = t2 – t1

Speed (v) A scalar The distance traveled by an object

during a given time interval divided by the time interval

V avg = Δd = d2 – d1

Δt t2 – t1

Speed (v) A scalar The distance traveled by an object

during a given time interval divided by the time interval

V avg = Δd = d2 – d1

Δt t2 – t1

Example: A car travelled a distance of 550m in a time interval of 35s. What is its speed?

Velocity (v) A vector The displacement of an object during

a time interval divided by the time interval

V avg = Δd = d2 – d1

Δt t2 – t1

Velocity (v)Example: Two trainers with stopwatches are timing a runner who is training for a race. Both timers start their stopwatches when the runner leaves the starting point. The first trainer is standing at a position that is 12m[S] of the starting point and the second trainer is 65m[S] of the starting point. Each trainer stops her stopwatch when the runner passes her. The first trainer’s stopwatch reads 1.6s and the second trainer’s stopwatch reads 8.7s. What is the athlete’s velocity with running between the trainers?

Using Tables and Graphs... Graphs are often used to represent the

motion of an object. Graphs are usually draw from the

information contained in a data table A table can be prepared by recording

observations of a moving object

Distance vs. Time

Distance(cm)

Time (s)Δd on the y-axis and Δt on the x-axis

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Once points are plotted on a

graph, sketch a line of

best fit.

Distance vs. TimeDistance (cm)

Time (s)Δd on the y-axis and Δt on the x-axis The slope of a graph is the rise divided

by the run of a line

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Once points are plotted on a graph, sketch a line of best fit.

RiseRun

Distance vs. Time Distance

(cm)

The slope of a graph is the rise divided by the run of a line Slope = Rise = Δd = cm = Speed Run Δt s

The slope of a Distance (cm) vs. Time (s) graph represents the SPEED of an object

The slope of a Displacement (cm [N] or [S]) vs. Time (s) represents the VELOCITY of an object

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Rise

Run

Slope = Rise = Δd = cm = Speed Run Δt s

WHAT’S THE VELOCITY??

Displacement (m[E])

Slope = Rise Run = Δd Δt = 60m[E] – 0.0m[E] 7.5s – 0.0s = 60m 7.5s = 8.0 m/s[E]

Time (s) 0 1 2 3 4 5 6 7 8

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WHAT’S THE VELOCITY??

Displacement (m[E])

Time (s)

Acceleration

A Vector QuantityA measure of the change in velocityover a time of period

Symbol = aUnits = m/s2

Two Ways to Accelerate an Object

1) Change the speed of the object2) Change the direction of an object

Calculating Accelerationa = v = v2 - v1

t t2 - t1

When an object speeds up, it shows positive acceleration

When an object slows down, it shows negative acceleration

Acceleration Question Example1) A train starts at rest and reaches a

speed of 54km/h in 10 seconds. What is its acceleration?

Acceleration Question Example2) An object starts from rest and

accelerates for a time of 12s. From 5.0 to 8.7 seconds, the car changes speed from 15 m/s to 27.8 m/s. Calculate the acceleration of the object during this time period.

Velocity vs. Time GraphVelocity vs Time

0

2

4

6

8

10

12

0 1 2 3 4 5 6

Time (s)

Velo

city

(m/s

)

Velocity vs. Time Graph The SLOPE of a

velocity-time graph gives you the ACCELERATION of the object

Velocity vs Time

0

2

4

6

8

10

12

0 1 2 3 4 5 6

Time (s)

Velo

city

(m/s

)

Velocity vs. Time Graph The SLOPE of a

velocity-time graph gives you the ACCELERATION of the object

The AREA under the line of a velocity-time graph gives you the DISPLACEMENT of the object

Velocity vs Time

0

2

4

6

8

10

12

0 1 2 3 4 5 6

Time (s)

Velo

city

(m/s

)

What is the acceleration?Slope = Rise = Δv = m/s = Acceleration Run Δt s ( a )

Velocity vs Time

0

2

4

6

8

10

12

0 1 2 3 4 5 6

Time (s)

Velo

city

(m/s

)

WORK INDIVIDUALLY FIND THE ACCELERATION?

Velocity (m/s[N])

Time (s)

0 1 2 3 4 5 6 7 8

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Graphs and Motion

Graphs and MotionGraphs can be used to show different

types of motion.

3 types of graphs that can show the same type of motion:

Distance vs. Time Velocity vs. Time Acceleration vs. Time

Type of Motion:An Object or Body at Rest

Distance vs. Time Velocity vs. Time Acceleration vs. Time

Type of Motion:An Object of Body in Uniform Motion

Distance vs. Time Velocity vs. Time Acceleration vs.

Time

Type of Motion:An Object or Body in Positive Uniform Motion

Distance vs. Time Velocity vs. Time Acceleration vs. Time

Type of Motion:An Object or Body in Negative Uniform Motion

Distance vs. Time Velocity vs. Time Acceleration vs. Time