Thursday, 13 April 2023

It is a change in the position of an object with respect to time.

Parameter Unit

Distance, d Meters, m

Time, t Seconds, s

Speed, vav Meters per second, ms-1

Displacement Meters, m

Velocity, v Meters per second, ms-1

Acceleration, a Meters per second per second, ms-2

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*Displacement is a vector and so must have a distance value andand a a direction.direction.

*Distance just has a value.

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*Velocity is also a vector and so must have a speed value and a and a directiondirection.

*Speed just has a value.

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*How much the speed is changing over time.

*Acceleration means speeding up, deceleration or negative acceleration is slowing down.

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Time from start (h)

Distance from Dunedin (km)

0 0

1.5 100

Changing tyre 2.0 100

4.5 275

Eating lunch 5.0 275

6.0 360

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A journey from Dunedin to Christchurch

When drawing graphs, follow these steps:

• Decide what data goes on the x-axis and what data goes on the y-axis.

• Title your graph and label the axes, remember to include units.

• Have even scales on your axes. (i.e. 1, 2, 3, 4 … not 1, 2, 5, 8 …)

• Plot your points on the graph. Make sure to start at 0.

• Connect points with a ruler for distance-time and speed-time graphs.

Draw a graph using this data.

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Hopefully yours looks something like this:

You have to be able to describe what is happening in a distance-time graph…

Handout

1. The vehicle covered 100km in the first two hours.

2. The vehicle was stationary between 2 hours and 5 hours.

3. Between 5 hours and 8 hours the vehicle covered a further 180 km.

4. Between 8 hours and 11 hours, the vehicle was stationary.

When reading a stopwatch you see…

00:02:30.15

1. How would you say this time??

2. How many seconds in this time?

3. How many minutes in this time?

1. Split into 2 groups.

2. Decide on 1 person to be each of the following:

• 3x Timekeepers

• 3x Recorders

• Runner

• Walker

3. On the field in the front of the school, each group will measure out a track of 30m.

4. The runner and walker both position themselves at the start. Both will set off at the same time.

5. One timekeeper is at the 10m mark, one at the 20m mark and one at the 30m mark. Each time keeper times when the runner and walker passes their mark .

6. Recorders will write down the times.

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Time at 0m (s)

Time at 10m (s)

Time at 20m (s)

Time at 30m (s)

Runner 0 2.40 3.00 5.00

Walker 0 6.00 12.00 19.00

*Speed measures the distance travelled in a given time.

time

distancev average

t

dvav

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vav

d

tHow to get kmh-1?Multiply ms-1 by 3.6Eg. 100ms-1 x 3.6

= 360kmh-1

*We can use the slopeslope of a distance – time graphs to find the speed of an object.

*To do this the graph line must be straight.straight.

Run

RiseSlope

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Handout

Calculate the slopeslope for each Car

*The average speed of Car A =

*The average speed of Car B =

*The average speed of Car C =

Time (h) Speedometer Car A (kmh-1)

0 50

0.5 50

1.0 50

1.5 50

2.0 50

2.5 50

3.0 50

3.5 50

4.0 50

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*Plot a speed – time graph using this data for Car A.

Speed (kmh-1)

Time (s)

Speedometer Car B (kmh-1)

80

80

80

0

0

0

80

80

80

• Just add another column to the table you have already drawn.

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*Just add the Car B data to the graph you already have.

*You will need to make the Car B line different to the Car A line.

*Use two colours or crosses and dots.

Speedometer Car C (kmh-1)

0

10

20

30

40

50

60

70

80

• Just add another column to the table you have already drawn.

*Just add the Car C data to the graph you already have.

*You will need to make the Car C line different to the Car A and Car B lines.

*Acceleration is a measure of how fast an object changes it’s speed.

in time change

speedin changeonAccelerati

t

va av

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vav

a t

Time (s) Speed Skier 1 (ms-1)

Speed Skier 2 (ms-1)

0 0 0

1 5 10

2 10 20

3 15 30

4 20 40

5 25 50

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*Plot a speed – time graph using this data.

*Plot the two skiers on the same axes.

*Draw a straight line of best fit for both skiers (use a ruler).

Speed (ms-1)

time (s)

*Calculate the slope of the two skiers.

*How quickly was skier 1 accelerating?

*How quickly was skier 2 accelerating?

Aim of the experiment:

To measure how the height of a ramp affects the speed of a marble covering 1m along flat ground.

Equipment:

•2x 1m rulers (one with a dip in it)

•Clamp stand

•Stopwatch

•Marble

Method:

Conduct this experiment in pairs (or groups of 3 max).

1.Measure a clamp stand so that it is 10cm above the ground.

2.Place a ruler on the clamp stand. This will work as the ramp.

3.At the end of the ramp (lying flat on the ground), place the second ruler.

4.Let the marble travel down the ramp.

5.Start timing the marble when it hits the flat surface, and time how long it takes to travel the 1m.

6.Repeat the experiment with the clamp at 10cm, so that you have 3 times.

7.Repeat the experiment with the clamp at 20cm, 30cm and 40cm. Make sure you have 3 times for each height.

Processing your data:

1.Average your times for each ramp height.

2.Draw a graph using the averages.

3.From your data, calculate the average speed of the marble for each ramp height.

4.Calculate the acceleration of the marble for each ramp height.

This is calculated from speed-time graphs.

Once you have split up your graph, use the formula to find the area of each shape:

Square or rectangle = x-axis X y-axis [base X height]

Triangle = ½ X(x-axis X y-axis) [½ X base X height]

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To do this, graphs need to be split into squares or rectangles or triangles.

You may have more than one shape on a graph.When this happens, work out the area of each shape separately and then add the areas together.

Handouts x2 – Finding the Area under Graphs and Distance from a speed-time graph

Km

Hours