B1.1 – 1.3 Average speed and average velocity Chapter B1

1.1 – Uniform Motion Motion is the movement of an object from one position to another.  It is considered uniform when an object is traveling in a straight line (no change of direction) at a constant speed (no +/ – acceleration).

1.1 – Uniform Motion An “ideal” situation – rarely occurs for long periods of time Other forces such as friction or air resistance interfere with uniform motion. Also, most objects will speed up, slow down or turn during its motion. Why most objects in the natural world move in non-uniform motion. When an object is stopped, it is still considered to have uniform motion because it still is at a constant speed (0 m/s).

Speed Average Speed (v) Represents the distance traveled over time, where –  d = total distance traveled –  t = time elapsed You do not need to specify direction. Measured in m/s (metres per second).

Speed Instantaneous Speed Unlike average speed, instantaneous speed is the speed an object is traveling at an instant of time.

Distance Traveled Distance traveled can be found in two ways: 1. The distance of each leg of the trip can be added up. » E.g. ∆d = d 1 + d 2 + d 3 … etc. 2. If the speed of the moving object is known & the time of travel, the distance can be found by rearranging the speed formula.

Distance Traveled Example #1: A driver talks on the phone for 36.0s while she is driving at 100km/h. How far does she travel in this time? 36.0s = 0.01h ∆d = v∆t = (100km/h)(0.01h) = 1km

Time Elapsed Calculating time elapsed  If the speed of the moving object is known and the distance the object travels, the time elapsed (gone by) can be found.

Time Elapsed Example #2: Standard headlights allow a driver to see up to 60m ahead of the car. If a car is traveling at 120km/h, how many seconds does a driver have between when they see a person on the side of the road, and when they pass the person? d = 60m = 0.06km ∆t = ∆d/v = 0.06km / 120km/h = h h = 1.8s

1.2 – Conversion Factors Converting between units Conversion factors allow you to convert from one unit to another (e.g. 100cm/1m, 60s/min). In science, most speeds are listed in meters per second, whereas in driving we use kilometers per hour.

1.2 – Conversion Factors To convert between m/s and km/h: 1 km= 1000 m =1000 m= 1000 m = 1 1 h 1 h60 min 3600 s 3.6 Bottom line: To convert from km/h to m/s  divide by 3.6 To convert from m/s to km/h  multiply by 3.6

Conversion Factors Example #3: Use the appropriate conversion factor to find out: – a) how many meters in 5.7cm? – b) how many m/s in 100km/h? – c) how many minutes in a week? a) (5.7cm)(1 m/100cm) = 0.057m b) (100km/h)(1000m/km)(1h / 3600s) = 27.8m/s c) (1 week)(7 days/week)(24 hours/day)(60 min/1hr) = min

1.3 - Scalar vs. Vector Quantities Scalar quantities are amounts that simply answer the question “how much.” – E.g. Temperature, distance traveled, average speed. Vector quantities not only describe “how much”, but also “in what direction” – E.g. Velocity, acceleration, displacement – The symbols for vector quantities are written with a single-barbed arrow. E.g. v, a, d

Distance Traveled vs. Displacement The distance traveled (d) of an object – Answers the question, “What is the total distance the object traveled?” – Found by adding up the distance of each leg of the trip, regardless of direction. – Describes the position or location of the object.

Distance Traveled vs. Displacement The displacement (  d) of an object. – Answers the question “how far away is the object from its starting point?” – In this case, the direction the object traveled does matter.

Distance Traveled vs. Displacement The displacement (  d) of an object. – If the object returns to its starting point, its displacement would be zero. If a journey has more than one leg, the resultant displacement is the vector sum of the individual legs (take the displacement along each leg and add them together).

Sign Convention Because direction matters in displacement or velocity calculations, typically one direction is assumed to be positive & the other, negative. Sign convention is an agreement about which direction is positive & and which is negative. Typically: – The following directions are positive: North, East, Right, Up – The following directions are negative: South, West, Left, Down

Sign Convention Example #4: Suppose a trucker drives from Calgary to Edmonton, a distance of 360km, then turns around to make a delivery in Red Deer. What is his distance traveled? What is his displacement? His distance traveled is the total distance that his truck traveled d = 360km + 180km = 540km His displacement is the difference between where he started, and where he ended up d = 360km [N] + (-180km [S]) = 180km [N]

Velocity v Represents the displacement over time, where  d = total displacement  t = time elapsed – Velocity is a vector quantity, you do need to specify direction. – Measured in m/s (metres per second).

Velocity v Example #5: A ball rolls 10.0m in 4.00s, bounces against a wall, then rolls 5.0m in 2.00s. What is the average speed of the ball? What is the velocity of the ball? v = (10.0m + 5.0m) = 15.0m = 2.5m/s (4.00s s) 6.00s v = (10.0m [right] – 5.0m [left]) = 5.0m [right] = 0.83m/s [right] (4.00s s) 6.00s