Displacement and Velocity Applied Physics 11

Position  Your position is the separation and direction from a reference point.  For example: 152 m [W]  [Direction in square brackets], usually a compass direction or a right/left or forward/back direction.  A quantity with a direction, such as position, is called a vector quantity.  Vector quantities must have M.U.D.  Magnitude or quantity  Units  Direction152 m [W]

Vector vs Scalar Quantities  Until now, we have used quantities that involve only size, not direction. These are called scalar quantities. Scalar Quantity distance∆d292 km time∆t3.0 h speedv23 m/s Vector Quantity position dd 2 km [E] from PWC displacement  ∆d 292 km [S] velocity vv 23 m/s [W]

Distance vs Displacement  Distance  Scalar quantity  "how much ground an object has covered" during its motion.  Displacement  Vector quantity  "how far out of place an object is”  the object's overall change in position.

Finding distance and displacement  A woman walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North.  She has walked 12 m in total  Distance = 12 m  She is back to her starting point  Displacement = 0 m

Distance vs Displacement  By car (and ferry), the distance travelled between St. John’s and Halifax is 1493km  After the journey, your total displacement would be about 882 km [SW]

Straight line diagrams  On a straight line, such as a street, position and displacement can be stated as negative or positive relative to a zero point.  This is a number line just like an x axis on a graph.  We call our starting point (our house) zero.  15 m to the right we will call the clothing store +15m  7 m to the left, we will call the photo shop -7 m

 If you travelled from your house to the clothing store, then back to the photo shop, what are your displacement and distance travelled?  ∆d = ∆d 2 - ∆d 1  Displacement = – 22 = -7 m  Distance = = 37 m

Vectors  A vector is a line segment that represents the size and direction of a vector quantity.  Vectors should communicate the size and direction of the quantity, and should always be labeled. 5 km [E]3 km [W]2 km [N]8 km [S]

Adding Vectors along a straight line  Rules for Adding Vectors: 1. State direction. Use compass symbol. 2. State your scale for magnitude. 3. Draw one of the vectors. 4. Join the second vector to the first by adding head to tail. 5. Draw the resultant vector from tail of the first vector to head of the second vector.

Adding Vectors Using Scale Diagrams  Anne take her dog for a walk. They walk 250 m [W] and then 215 m [E] before stopping to talk to a neighbour. Draw a vector diagram to find their resultant displacement at this point. 250 m [W] 215 m [E]35 m [W]

Adding Vectors Algebraically  Susan and Peter go for a walk. They travel 250 m [E] and then went 500 m [W].  What is the resultant displacement?  East will be positive and West negative. → → →  ∆d = ∆d 1 + ∆d 2 →  ∆d = 250 m m →  ∆d = m = 250m [W]

Adding Vectors on an Angle  When adding vectors that are not along the same line, we follow many of the same steps.  Vectors are drawn to scale and in the proper direction.  Add vectors head to tail.  Draw resultant vector tail to tail, head to head.

 Measure resultant vector and determine displacement by using your scale.  Measure the angle with a protractor. The angle to be measured is the angle where the end of the resultant vector joins with the end of the first vector.

Representing angles

Question  A car travels 60 km (N), then 30 km (E). What is the displacement of the car?

Question 2  A ball is thrown 4m west, then 3 meters south.

Velocity  Speed is a scalar quantity.  Velocity includes a direction, and is a vector quantity.  Velocity is the change in displacement (another vector quantity) in a given time.  The direction of the velocity is always the same as the direction of the displacement.

Sample Problem 1  A train travels at a constant speed through the countryside and has a displacement of 150 km [E] in a time of 1.7 h. What is the velocity of the train?  ∆d = 150 km [E]  ∆t = 1.7 h  v = ?  v = ∆d/∆t  = 150 km [E]/ 1.7 h  = 88 km/h [E]

Average Velocity  Average velocity is defined as the overall rate of change of position from start to finish.  It is calculated by dividing the resultant displacement by the total time.  Average velocity does not depend on the path taken or the speeds throughout the path.

Sample Problem 2  Monarch butterflies migrate from Eastern Canada to Mexico, a resultant displacement of 3500 km [SW] in a time of 91 d. What is their average velocity in km/h?

Average Speed vs Average Velocity  A jogger runs 52 m [E] in 10.0 s and then 41 m [W] for 8.0s. What is his average velocity?  The average velocity depends only on the resultant displacement and total time, not on the individual velocities.

How is this different from average speed?  A jogger runs 52 m [E] in 10.0 s and then 41 m [W] for 8.0s. What is his average speed?  Remember that in this case, we are looking for the total distance travelled over the total time.

Speed vs Velocity A jogger runs 52 m [E] in 10.0 s and then 41 m [W] for 8.0s  Average speed  5.2 m/s  Average velocity  0.61 m/s [E]