1. Dynamics and Space Velocity and displacement Vectors and scalars

2. Learning Outcomes Vector and scalar quantities: force, speed, velocity, distance, displacement, acceleration, mass, time and energy. Calculation of the resultant of two vector quantities in one dimension or at right angles. Determination of displacement and/or distance using scale diagram or calculation Use of appropriate relationships to calculate velocity in one direction.

3. Lesson 1 1.Define what is meant by vector and scalar quantities. 2.Describe the difference between distance and displacement and speed and velocity. 3.Calculate the resultant of two vector quantities at right angles to one another.

4. Scalar And Vector Quantities All physical quantities can be divided into two groups – vectors or scalars. When determining if a quantity is a vector or a scalar you need only ask one question, does direction matter? A scalar quantity has size (magnitude) only. A vector quantity has both size and direction.

5. Distance and Displacement Distance, d, is how far an object has travelled between two points, regardless of direction. It is a scalar and is measured in metres. Displacement, s, is the shortest distance travelled between two points in a straight line. It is a vector measured in metres and in a particular direction.

6. Speed and Velocity Speed and velocity can be calculated by using the following equations: Speed = distancevelocity = displacement time time where speed is a scalar and velocity is a vector. The direction of the velocity will be the same as that calculated for displacement.

7. Example 1 A boy walks 40 m north, then turns back south for 10 m. The journey takes 20 seconds. What is a)the displacement of the boy b)the distance the boy travelled c)the average velocity d)the average speed a)s = 40–10 = 30 m north b)d = 40 + 10 = 50 m c)v = s / t = 30 / 20 = 1.5 m/s north d)v = d / t = 50 / 20 = 2.5 m/s

8. Example 2 A car drives 60 km north, then 80 km east, as shown in the diagram. The journey takes 2 hours. Calculate (in km or km/h): a)the distance travelled b)the displacement c)the average speed d)the average velocity a)d = 80 + 60 = 140 km b)s 2 = 80 2 + 60 2 s = 100 km tan Θ = 80 / 60 Θ = 53 0 W of N / (053) c)v = d / t = 140 / 2 = 70 km/h d)v = s / t = 100 / 2 = 50 km/h (053) NB: The method used for part b) can also be used to work out resultant forces at right angles.

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12. Lesson 2 1.Define what is meant by vector and scalar quantities. 2.Investigate different quantities to determine if they are vector or scalar. 3.Identify vector quantities and scalar quantities.

13. Experiment You can now carry out experiments to determine if the following quantities are vectors or scalars: Vector or scalar? QuantityPredictionObservation Mass Force Acceleration Time Energy

14. Examples of Vectors and Scalars VectorsScalars Velocity Displacement Acceleration Force Speed Distance Mass Time Energy (all types)

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19. Lesson 3 1.Describe how to measure the average speed of an object. 2.Carry out calculations on the above.

20. Average Speed The average speed of a body is found by dividing the total distance travelled by the time of the whole journey. v=dv=d t

21. Experiment TaskDistance covered (m) Time taken (s) Average speed (m/s) Walking Your choice from: Running / hopping / backwards walk etc Measure out a distance and record the time taken to travel that distance. Use the results obtained to calculate your average speed in the table below.

22. How to measure average speed (3 marks) 1.Measure out a distance (½) using a ruler (½). 2.Record the time taken to travel the distance (½) using a stopwatch (½). 3.Use the equation: v=dv=d t(1)

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24. Thinker Do you know your average speeds?

25. Lesson 4 1.Describe how to measure the instantaneous speed of an object. 2.Carry out calculations on the above.

26. Instantaneous Speed Instantaneous speed is the speed of an object at a particular instance in time. It is also calculated using v = d / t. The instantaneous speed is measured over a very small distance and time period.

27. Experiment

28. Measuring Instantaneous Speed 1.Record the length of the mask on the trolley, d, in metres. 2.Release trolley down slope. 3.Trolley cuts light gate which then allows the electronic timer to record time, t, in seconds. 4.Instantaneous speed, v, is calculated using v = d / t.

29. Experiment Length of mask =m Distance up slope (m) Time taken for mask to pass through light gate (s) Instantaneous speed (m/s) 0.25 0.50 0.75 1.00

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32. Summary Velocity and displacement You should now be able to do the following: Identify vector and scalar quantities from the following: force, speed, velocity, distance, displacement, acceleration, mass, time and energy. Calculate the resultant of two vector quantities in one dimension or at right angles. Determine the displacement and/or distance using scale diagram or calculation. Use of appropriate relationships to calculate velocity in one direction.