5 Vector or Scalar?We use pictures to represent vector quantities, specifically arrows.The arrow direction indicates…direction.The length of the arrow is drawn to scale and represents the magnitude of the quantity.
6 Vector or ScalarEx: A car traveling to the right at 5m/s and a car traveling to the left at 10m/sObserve how the 10m/s arrow is twice the length of the 5m/s arrow.
7 Adding VectorsVectors can be added like a scalar quantity can be added, however, the direction determine the final answer:In one-dimensional motion:Forward or up is labeled as positiveBackward or down is labeled as negativeVectors are always added. Sometimes we are just adding a negative quantity.
8 Adding Vectors Consider an airplane flying east (positive) at 100km/h: The airplane encounters a wind blowing with the plane (positive) at 20km/h.Add the vectors ‘tip to tail’Connect the tip of the first to the tail of the secondAdd togetherThe resultant vector is the result of adding the two magnitudes. (120km/h)
9 Adding VectorsNow consider the same airplane flying east (positive) at 100km/h:The airplane now encounters a wind blowing against the plane (negative) at 20km/h.Add the vectors ‘tip to tail’The resultant vector again is the result of adding the two magnitudes together. (80km/h)
10 Adding VectorsThe result vector has the direction of the largest magnitude vector. (positive or negative)The result vector magnitude is the sum of all the magnitudes (with positive and negative directions) added together.
11 Adding Vectors Examples: A runner on a treadmill is running at 10m/s and the treadmill belt is circling at 10m/s in the opposite direction.Total velocity of runner = 0m/sA boat is traveling downstream at 16m/s with a current of 3m/s.Total velocity of boat = 19m/sA boat is traveling upstream at 18m/s against a current of 8m/s.Total velocity of boat = 10m/s
12 Distance vs. Displacement Our quantity of distance (from the last sections) was a scalar quantity. We were not looking at the direction of motion.When direction is taken into account, you are looking at displacement.Distance is the total area covered while movingDisplacement is the direct line path’s length.
13 Distance vs. Displacement Observe:A person starts at 0m, and then moves back 3 meters, then moves forward 2m, then moves forwards another 3m, then moves backwards 6m.What is the person’s distance and displacement?Distance = 14m = 3m + 2m + 3m + 6mDisplacement = -4m = -3m + 2m + 3m + -6mA person starts at 0m, and then moves back 2 meters, then moves forward 3m.What is the person’s distance and displacement?Distance = 5m = 2m + 3mDisplacement = 1m = -2m +3m
14 Distance vs. Displacement Distance = the sum of all movement takenDistance: x = x1 + x2 + x3 + …Displacement = the difference between the final position and the initial position.Displacement x = xf – xi
15 Speed & VelocitySpeed and velocity are both looking at how quickly something is moving, however velocity is also looking at direction.Speed: Scalar (magnitude only)Velocity: Vector (magnitude and direction)Ex:Traveling at 60km/h (speed)Traveling north at 60km/h (velocity)
16 VelocityVelocity is determined by dividing the displacement by the time taken.velocity = displacement/timev = (xf-xi)/tExample:You start at 0m, move forward 3m, and move back 1m. This takes 2.4 seconds. Determine your velocity.V = 0.83m/s
17 VelocityWhen motion is only in one dimension, direction is indicated as being in the positive or negative direction, such as on a number line.A negative velocity is pointing in the negative direction, a positive velocity is pointing in the positive direction.
18 Constant VelocityFrom the definition of velocity, having a constant velocity requires constant magnitude speed and constant direction.Constant direction must be in a straight line.Motion at constant velocity is motion in a straight line at constant speed.
19 Changing VelocityVelocity changes whenever speed or direction (or both) changes.Constant speed and constant velocity are not the same thing.You can be traveling at a constant speed while continually changing your direction.
20 AccelerationWe can change the state of motion of an object by changing its speed or direction of motion (or both).The rate at which velocity changes is called acceleration.Acceleration is a rate-> change over time.Acceleration = change in velocity time
21 Acceleration Specifically: Acceleration = Final velocity – Initial velocity Timea = vf – vi tExamples: A car accelerates from 20.0m/s to 33.2m/s in 7.40s. Determine the acceleration.1.78m/s2
22 AccelerationThe unit of acceleration is the meter per second per second, also said as the meter per second squared.Acceleration can also be negative, also referred to as deceleration, this simply means that the object is slowing down.
23 AccelerationBut if we don’t have final velocity, initial velocity, acceleration, or time, we can substitute and rearrange to get new formulas to use.Looking at these formulas, you choose which one has what you are looking for and what you are not given.
24 Formulasv = x a = vf – vi t tx = vit + ½ at2Vf2 = vi2 + 2ax
25 ExamplesDetermine the acceleration of a car that accelerates from rest to 20.0m/s in 4 seconds.5m/s2A car is traveling at 30.0m/s and slams on the brakes. It takes 4.5 seconds to stop. Determine the acceleration.-6.7m/s2
26 ExamplesA car accelerates from 8.99m/s at 2.3m/s2 for 3.00s. How far will the car travel? What is the final velocity of the car?X = 37mVf = 16m/s
27 ExamplesA sprinter is on a 1.00x102m track and accelerates at 1.22m/s2 to his top speed in 4.56s. What is is starting speed?A car travels 32kilometers. The car started at 8.55km/h and accelerates to 25km/h. Determine the car’s acceleration.