2SCALARS?A scalar is a quantity which has magnitude (number value) onlyExamples of scalars are speed, distance, energy, charge, volume, mass, weight and temperature.The value of a scalar is called its magnitude. Scalar quantities can be directly added or subtracted from each other
3VECTORS?A vector is a quantity which has both a magnitude and a direction.Examples of vectors are displacement, velocity, and acceleration.Vectors cannot be added in the same way as scalars!
4VECTOR NOTATIONVectors are represented by an arrow on top of the symbol. Below is an example of velocity, which is a vector.v
6Hold up either “S” or “V” Sheri throws the ball 20m up
7When a direction is written in a vector description, it is usually abbreviated and put into square brackets.[W] is west [E] is east[N] is north [S] is south
8DIRECTION & DISTANCE Distance: Length of path which a body covers during motionUnits: metre (m) or kilometer (km)Displacement:The change in position of an object during motion.Distance is a scalar,and displacement is a vector variable.
9Displacement (blue line) is how far the object is from its starting point, regardless of how it got there.Distance traveled (dashed line) is measured along the actual path.
10When calculating displacement North is positive, South is negativeEast is positive, West is negativeUp is positive, Down is negativeRight is positive, Left is negative
11- DISPLACEMENT FORMULA d d d The formula for displacement is: This formula means the “change in position” is equal to the final position minus the initial position. The answer is written with the magnitude first, and the direction in square brackets second.For example: 40 km [E]dd-d=if
12DISPLACEMENT FORMULA EXAMPLE John rode his bicycle from point that was 3 km west of a point and stopped at a place located 12 km east of that point. Calculate his displacement.Answer: 15 km [E]3km12km
13MATHEMATICAL EXAMPLE OF DISTANCE AND DISPLACEMENT #2 Wendy rides her bike 10km North. Then she goes 8 km East and finally 4 km South.What is Wendy’s Displacement?What is Wendy’s Distance?10km [NE]6km [N], 8km [E]22km
14A NOTE WITH DISPLACEMENT WATCH FOR SIGNS (+ OR - )CHOOSE A REFERENCE DIRECTION AS POSITIVEBE CONSISTENT WITH YOUR SIGNS!
15TIME INTERVALStInitial Time is the time when an event starts.Final Time is the time when the event ends.The time interval ∆t is the total time of the event.Note: ∆ means changeitftt-t=fi
16CONCEPTUAL TIME EXAMPLE #1 A show starts at 8:25 and ends at 8:52.What is the shows time interval?27 min
17WHAT IS UNIFORM MOTIONUniform motion is when you travel equal displacements in equal time intervalsThis rarely happens in real life, but it is a good approximation.
18Which one is Uniform Motion? X X X X X X X XX X X X X X X
198.1 Continued: POSITION – TIME GRAPHS WITH UNIFORM MOTION
20Describes the rate of change in position of an object over time
23The reference point (origin) is needed so we know which way is positive, which way is negative, and where zero is.Reference pointReference point is where the x and y axis intersect
24Positive Slope: The object is moving in the positive direction, and its position is increasing with time.This also means that the object has a positive velocity (has a speed in the positive direction)
25Negative Slope: The object is moving in the negative direction, and its position is decreasing with time.This also means that the object has a negative velocity (has a speed in the negative direction)
26Zero Slope: The object is at rest. The object is not moving.The position is not changing.
27If an object is staying in the same position for a time interval than its… at reststoppednot movingstillRepresented by a horizontal line on a position vs time graph
282) When and where is the object not moving? position3 m2 m1 m0 m8 s4 s6 s10 s0 s2 stime
291)The object is at rest at 4 m position2 m1 m0 m2.0 s1.0 s1.5 s2.5s0 s0.5 stime
30The object who turned around at 4 seconds 5 m4 m3 mposition2 m1 m0 m8 s4 s6 s10 s0 s2 stime
32SPEED AND VELOCITY, WHATS THE DIFFERENCE? Can two objects have the same speed and different velocities?Velocity is a vector – has direction and magnitudeSpeed is a scalar, it only has magnitude.(move in different directions) YES
33AVERAGE VELOCITYAverage velocity is equal to the change in position (displacement) divided by the change in time.This is why velocity has the units (m/s)
34AVERAGE VELOCITY In a way, average velocity is a simplification. It tells us on average over a certain time interval how fast an object is moving.It does not tell us exactly what velocity the object moved at for all instants in that interval.
35DIFFERENCE BETWEEN AVERAGE VELOCITY AND AVERAGE SPEED. I walk 10 m North in 5 seconds and then walk for 10 m South in the next 5 seconds.What is my average velocity?My average speed?0 m/s20m = 2 m/s10s
36Calculating Average Velocity The relationship between average velocity, displacement, and time is:What is the average velocity of a dog that takes 4.0 s to run forward 14 m?(3.5 m/s forward)A boat travels 280 m east in a time of 120 s. What is the boat’s average velocity?(2.3 m/s east)
37CONVERTING UNITS: m/s <-> km/h For example, convert 75 km/h to m/s.
38PROBLEM #1What is the average velocity of a skateboard that goes 50 m [W] over a time interval of 8 seconds?Answer:Average Velocity = 6.25 m/s [W]
39PROBLEM #2A deer is running forward at a speed of 46 km/h. How far does it travel in 30 seconds?Displacement = km or 384 meters
40PROBLEM #3How many minutes would it take a car moving at an average velocity of km / h to travel 125 km?Time = 91.5 minutes
41AccelerationAcceleration (a) is the rate of change in velocity (how fast velocity changes)This change in velocity can be due to a change in speed and/or a change in direction.Two objects with the same change in velocity can have different accelerations.This is because acceleration describes the rate at which the change in velocity occurs.Suppose both of these vehicles, starting from rest, speed up to 60 km/h. They will have the same change in velocity, but, since the dragster can get to 60 km/h faster than the old car, the dragster will have a greater acceleration.
42Positive and Negative Acceleration The direction of the acceleration is the same as the direction of the change in velocity.Acceleration that is opposite the direction of motion is sometimes called deceleration.
43Examples of acceleration: Acceleration can be described in a velocity-time graph. BE CAREFUL not to confuse this with a position-time graph!Examples of acceleration:1. A car speeding up in the forward directionIf we designate the forward direction as positive (+), then the change in velocity is positive (+), therefore the acceleration is positive (+).
44Examples of acceleration: 2. A car slowing down in the forward direction.If we designate the forward direction as positive (+), then the change in velocity is negative (-), therefore the acceleration is negative (-).
45Examples of acceleration: 3. A car speeding up in the backward direction.If we designate the backward direction as negative (-) then the change in velocity is negative (-).This means that the acceleration is negative (-) even though the car is increasing its speed.Remember positive (+) and negative (-) refer to directions!!!!
46Examples of acceleration: 4. A car slowing down in the backward direction.If we designate the backward direction as negative (-) then the change in velocity is positive (+).This means that the acceleration is positive (+) even though the car is decreasing its speed.Remember positive (+) and negative (-) refer to directions.
47Zero Acceleration Examples of acceleration: 5. A car is stopped. The change in velocity is zero. The car is at rest.This means that the acceleration is zero.
48Examples of acceleration: 6. A car has constant velocity (uniform motion).The change in velocity is zero.This means that the acceleration is zero. The car is not speeding up or slowing down, but moving at constant velocity.
49CalculateBus is moving 15 m/s backwards and slows down to m/s backwards.Train is moving 300 km/h forwards and speeds up to 400 km/h forward.Car starts at 5 m/s forwards and finishes at m/s backwards.Jeep is moving 8 m/s backwards and slows to a stop.
509.2 Calculating Acceleration The acceleration of an object depends on the change in velocity and the time required to change the velocity.When stopping a moving object, the relationship between time and acceleration is:Increasing the stopping time decreases the acceleration.Decreasing the stopping time increases the acceleration.
51Velocity-Time GraphsThe motion of an object with a changing velocity can be represented by a velocity-time graph.The slope of a velocity-time graph is average acceleration.Acceleration is measured in m/s2.
52Determining Motion from a Velocity-Time Graph A velocity-time graph can be analyzed to describe the motion of an object.Positive slope (positive acceleration) – object’s velocity is increasing in the positive directionZero slope (zero acceleration) – object’s velocity is constantNegative slope (negative acceleration) – object’s velocity is decreasing in the positive direction or the object’s velocity is increasing in the negative direction
53Calculating Acceleration The relationship of acceleration, change in velocity, and time interval is given by the equation:Example:A pool ball travelling at 2.5 m/s towards the cushion bounces off at 1.5 m/s. If the ball was in contact with the cushion for 0.20 s, what is the ball’s acceleration? Assume towards the cushion is the positive direction. (+)
54Calculating Acceleration Try the following acceleration problems.A truck starting from rest accelerates uniformly to 18 m/s [W] in 4.5 s What is the trucks acceleration?A toboggan moving 5.0 m/s forward decelerates backward at m/s2 for 10 s. What is the toboggans velocity at the end of the 10 s?How much time does it take a car travelling south at 12 m/s to increase its velocity to 26 m/s south if it accelerates at m/s2 south?
56Gravity and Acceleration Objects near the surface of Earth fall to Earth due to the force of gravity.Gravity is a pulling force that acts between two or more masses.Air resistance is a friction-like force that opposes the motion of objects that move through the air.Ignoring air resistance, all objects will accelerate towards Earth at the same rate.The acceleration due to gravity is 9.8 m/s2 downward.
57Calculating Motion Due to Gravity To analyze situation where objects are accelerating due to gravity, use the equations:In these equations, the acceleration ( ) is 9.8 m/s2 downward.Example:Suppose a rock falls from the top of a cliff. What is the change in velocity of the rock after it has fallen for 1.5 s? Assign “down” as negative (-).
58Calculating Motion Due to Gravity Try the following acceleration due to gravity problems.What is the change in velocity of a brick that falls for 3.5 s?A ball is thrown straight up into the air at 14 m/s. How long does it take for the ball to slow down to an upward velocity of 6.0 m/s?A rock is thrown downwards with an initial velocity of 8.0 m/s. What is the velocity of the rock after 1.5 s?