Learning Outcomes. Distinguish between Distance and Displacement when comparing positions. Distinguish between Scalar and Vector Quantities

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1 Dr Pusey

2 Learning Outcomes Distinguish between Distance and Displacement when comparing positions Distinguish between Scalar and Vector Quantities Add and subtract vectors in one and two dimensions

3 What are 1, 2 and 3 dimensional space? Think of it like this: 1 Dimensional (1D) - sideways 2 Dimensional (2D) - sideways and upwards 3 Dimensional (3D) sideways, upwards and into!

4 Vectors and Scalars Scalars Magnitude only Vectors Magnitude AND direction Examples Distance (20 m) Speed (10 m/s) Mass (30 kg) Examples Displacement (20 m North) Velocity (10 m/s Eastwards) Weight (20 N Downwards) No Joke! Weight is a Force, Forces are Vectors

5 Check your understanding Example Scalar or Vector? 5 m 30 m/s, East 5 km, North 20 degrees Celsius 256 bytes 4000 Calories

6 Check your understanding Example 5 m 30 m/s, East 5 km, North 20 degrees Celsius 256 bytes 4000 Calories Scalar or Vector? This is a scalar; there is no direction listed for it. This is a vector; a direction is listed for it. This is a vector; a direction is listed for it. This is a scalar; there is no direction listed for it. This is a scalar; there is no direction listed for it. This is a scalar; there is no direction listed for it.

7 Examples of Scalars and Vectors Mass Momentum Velocity Weight Work Length Distance Displacement Speed Velocity Power Energy Acceleration Force Friction Scalar Vector

8 Examples of Scalars and Vectors Scalar Mass Length Distance Speed Power Energy Work Vector Displacement Velocity Acceleration Force Weight Friction Momentum

9 Distance vs Displacement Distance is a scalar quantity that refers to how much ground an object has covered during its motion. Displacement is a vector quantity that refers to how far out of place an object is ; it is the object's overall change in position.

10 Adding Vectors Example 1 A student walks 5 m forwards and then 5 m backwards. What distance did she travel? What is her displacement?

11 Adding Vectors Example 1 A student walks 5 m forwards and then 5 m backwards. What distance did she travel? 5 m + 5 m = 10 m What is her displacement? 5 m 0 m 5 m

12 Distance and Displacement Distance: The total path Displacement: The difference in position from the start

13 Position, Distance, Displacement Home School 7 km 6 km Beach A student walks to the Beach for a quick surf in the morning and then back to School to start his day. 3 km A) What distance did he travel? B) What is his displacement? Cinemas

14 Position, Distance, Displacement Home School 7 km 6 km Distance Beach Displacement Distance 3 km A) What distance did he travel? = 19km B) What is his displacement? 7km East Cinemas

15 Position, Distance, Displacement Home School 7 km 6 km Beach He then decides to go and watch the latest vampire / goth movie with his mates after school. 3 km What is the total distance travelled? What is the displacement of the student? Total: HOME BEACH SCHOOL CINEMAS Cinemas

16 Position, Distance, Displacement Home School 7 km 6 km Beach Distance: Beach (13km) +School (6km) +Cinema (6.7km) =6.7km 3 km = 25.7km

17 Displacement: Vector Addition Home School 7 km 6 km Beach =13.3 km 3 km Displacement = 13.3 km SOUTH-EAST

18 HELP! LOST DRONE! Dr Pusey s SupaTEK Drone s GPS has failed and we are trying to work out where it currently is so we can give co-ordinates to bring it home! The telemetry data shows the following sequence of vectors: 7km North 4km East 3km South 8km West What two vectors would bring the drone home? MEGA BONUS POINTS What ONE vector would bring the drone home?

19 HELP! LOST DRONE! 7km North 4km East 3km South 8km West First: Stack the vectors up (head to toe) and draw the RESULTANT VECTOR This is the Displacement Vector 8km 4km 3km Resultant Vector 7km

20 HELP! LOST DRONE! Work out how far North and East the drone is using graph paper. OR, Simply add up the North and East components separately. 7km 3km = 4 km North 4km 8km = -4 km East = 4 km West 4km 8km 2km 4km Resultant Vector 7km 4km

21 Bring it home 2 Vectors to Return: =4km East and 4km South 4km 1 Vector to Return: = = 5.66 km 4km =5.66 km South-East

22 How did you go? Distinguish between Distance and Displacement when comparing positions Distinguish between Scalar and Vector Quantities Add and subtract vectors in one and two dimensions

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