Physics: Describing Motion

Our Perception of Motion Travelling from Edmonton to Calgary takes 3 hours by car and less than an hour by plane How long would it take if you walked? In each case, the distance travelled in the same. The difference is the average speed of each mode of transportation.

One-Dimensional Kinematics Kinematics is the mathematical description of motion. Describing motion accurately is the first step towards understanding it. In this unit, we will consider one- dimensional motion, which is motion on a line. There are only two possible directions: Up or down Right or left

Scalars A scalar quantity is a quantity consisting of magnitude (how much) only, but does not take direction into consideration –Examples: Time, distance, speed are scalars Scalar Not Scalar

Average Speed (Scalar Quantity) Total distance travelled over a specified time total distance traveled by the object (m) total time of the trip (s) Average speed (m/s) Standard Units: m/s This formula is on page 2 of your data booklet

Average Speed Example 1 Using the endpoint of the cyclists shown below, determine their average speed

Uniform Motion Notice some interesting features about the graph from the previous question... –The car is the only one that produced a straight line –Why is this? –Because it is travelling with uniform motion – probably on cruise control! Uniform Motion: Motion in a straight line at a constant speed. Nonuniform Motion: Motion with a change in speed, direction or both.

Instantaneous Speed Speed at an instant of time –Highway 2 between Edmonton and Calgary has a speed limit of 110 km/h. –Most cars don’t travel at exactly that speed. These speed limits refer to the instantaneous speed of the vehicle NOT the average speed

Average Speed Example 2 An owl is able to drop 1.30m in 0.91s to capture food. Determine the owl’s average speed during its descent in m/s. Can you convert this to km/h???

Average Speed Example 2 An owl is able to drop 1.30m in 0.91s to capture food. Determine the owl’s average speed during its descent in km/h. Or we could multiply by 3.6

Average Speed Example 3 During an intense sneeze, a drivers’ eyes can remain closed for about 0.50s. If a vehicle is moving 100km/h, how many meters does the car travel during this time? This is equivalent to 3 car lengths!!!

Average Speed Example 4 Dana reaches into the backseat to grab a CD. If she takes her eyes off the road for 2.0s, determine the number of meters she would travel if her car was moving 50 km/h. 50km/h is the max speed in a residential area. This is equivalent to 7 car lengths!!!

Average Speed Example 5 Dana reaches into the backseat to grab a CD. If she takes her eyes off the road for 2.0s, determine the number of meters she would travel if her car was moving 110 km/h. 110 km/h is the max speed on most highways. This is equivalent to 15 car lengths!!!

Average Speed Example 6 While driving down a dark road, the headlights on Ryan’s truck allow him to see up to 60m of the road ahead. If he is travelling 70km/h, how many seconds will it take Manpreet to reach the furthest point of his headlight’s beam?

Vectors A vector is a quantity consisting of magnitude PLUS direction –Examples: Displacement, velocity, and acceleration are vector quantities –In all of these, position (location) matters Vector Scalar

Importance of Vectors Consider the two movements below Each takes 1 minute to complete –In terms of time, distance, and speed (scalars), both motions are exactly the same –But clearly both motions are very different! 100 m 50 m The difference is the direction of movement.

Vector Notation There are 3 ways to represent a 1-D vector in physics: 1. By description…John Creek is 5.0km north 2. Using an arrow (shown below) 3. Using a number (with a reference system) In all three, you are taking position (location) into account Base camp to… Distance (scalar) Position (vector) John Creekd=5.0km Scalzo Creekd=5.0km 5.0km North 5.0km South

Vector Notation 3. Using a number (with a reference system) Sign Convention Position from base camp to… John CreekScalzo Creek 5.0km North 5.0km South

Displacement Displacement is the change in position (location) of an object. It is the straight-line distance from the initial position to the final position. i.e. the "start-to-finish" vector The symbol for displacement includes the Greek letter delta ( Δ ) which is short for “change in”. Δ d

Distance vs. Displacement Distance (d) is scalar, which means it has no direction (i.e. How far you walked to get from start to finish) Displacement (d) is a vector, which means it has both magnitude and direction (i.e. The straight line distance from start to finish) Δ d Distance, d

Distance vs. Displacement Example 1: Motion in one direction A person walks 10 m towards the West. What is the distance and displacement? Distance: d = 10 m Displacement: d = 10 m West If motion goes in one direction, then there is only one difference between distance and displacement: Displacement is a vector, so must indicate its direction. They have the same magnitude. 10 m

Distance vs. Displacement Example 2: Motion that changes direction A person walks 20 m North, and then walks 20m South –What is the overall distance and displacement Overall Distance: d T = 20 m + 20 m d T = 40 m Distance is a scalar, so the numbers are always positive (magnitudes only) 20 m

Distance vs. Displacement Example 2: Motion that changes direction A person walks 20 m North, and then walks 20m South –What is the overall distance and displacement Overall Displacement: Δ d T = +20 m + (-20 m) Δ d T = 0 m Displacement is a vector, so you have to show direction. When the object moves North, it is a positive displacement When it moves South, it is a negative displacement. Reference System: North is positive / South is negative Start Finish Overall displacement is the “start-to-finish” vector. Since the object returns to its original position, it has no overall displacement. 20 m

Displacement: Example 3 An object moves 42.8 m North and then 67.1 m South. Compare the distance and displacement. Overall distance: d T = 42.8 m m 42.8 m 67.1 m = m Distance is a scalar. Thus, everything is positive.

Overall displacement:Ref: North is positive South is negative Δ d T = (+42.8 m) + (-67.1 m) = m m m = 24.3 m South of its original position Be certain to identify the direction of the displacement. Displacement: Example 3

Average Velocity A vector quantity describing the change in position (displacement) over a specified period of time Not the same as speed!! Velocity is similar to speed but always indicates the direction the object is travelling displacement (m) total time of the trip (s) Average velocity (m/s) Standard Units: m/s

Average Velocity Scalars Scalar QuantitiesScalar Equation Distance, d Time, t Average speed, v Vectors Vector Quantities Displacement, Δd Average velocity, v

Average Velocity Ex 1 If Sara travels 13.5 km along the trail from the John Creek Crossing to the Nick Brook Crossing in 3.5 h, what is Sara’s average velocity for the trip in km/h?

Average Velocity Example 2 Use the graph below and a ruler to answer the next question Determine the position of each of the following locations from the reference point. Describe the direction in terns of east and west and by using sign convention. A) Bird Creek B) Elk Creek 6cm = 6 x 3 = 18 km [W] 7cm = 7 x 3 = 21 km [E] 6 cm 7 cm

Uniform Motion Uniform motion is when an object is travelling at a constant speed and in a constant direction. Slope of a d-t graph is velocity Uniform motion = constant velocity = constant slope

Position-Time Graphs You can determine average velocity using a position- time graph’s slope as follows:

Position-Time Graph Examples For each graph, describe each motion and determine the average velocity of the motion.

You can determine the displacement with a velocity-time graph. Velocity-Time Graphs

Velocity-Time Graph Examples For each graph, describe each motion and determine the displacement of the tool during this trial

Acceleration Acceleration is the change in velocity over time –I.e. How fast you speed up or slow down Graphs describing an object speeding up are different from graphs that describe an object moving with uniform motion.

The velocity-time graph is a straight line from which it is easy to determine slope. The slope of a velocity-time graph is called acceleration Acceleration

Units: m/s 2

Uniform Acceleration Acceleration described by a sloping, straight line on a velocity-time graph Not all velocity-time graphs produce a straight line like this one When a graph is not a straight line, average acceleration must be determined!!

Acceleration Example 1 Calculate the acceleration from the graph below. –HINT: Choose any two points from the best fit line. (1.20s, 15.0cm/s) (5.00s, 39.0cm/s)

Acceleration Example 2 Determine the acceleration using the information provided by each of the following graphs

Acceleration Example 3 A car travelling 70 km/h east changes its velocity to 90 km/h east in 4.5 s. Determine the magnitude and direction of the average acceleration of the car in m/s 2.

Acceleration Example 4 A sprinter on a high school track team can achieve an average acceleration of 3.0 m/s 2 from rest to his maximum velocity of 11.0m/s. –Calculate the time taken by the sprinter to reach his maximum velocity

Acceleration Example 4 A sprinter on a high school track team can achieve an average acceleration of 3.0 m/s 2 from rest to his maximum velocity of 11.0m/s. –The coach explained during training that the sprinter can improve his performance if he can increase his acceleration during the first phase of the race. Even if his maximum velocity remained the same, a higher rate of acceleration would give him better results. Explain this thinking by referring to the calculation from the previous slide. As the solution to previous slide indicates, a higher rate of acceleration means that the sprinter will reach his maximum velocity in less time. This means that this athlete would spend more time racing at his maximum velocity, allowing him to finish the race sooner.

Acceleration Example 5 A group of teens riding an inflatable tube start from rest and travel down a hill, accelerating at an average rate of 1.15 m/s 2. Determine the speed reached by the teens after travelling for 6.0s. Since the velocity and acceleration vectors both point in the same direction and the question is asking for speed (a scalar), the vector notation is not necessary.

Acceleration Example 6 At a drag race, the dragsters start from rest and race down a course about 400 m long. In one race, a competitor drove with an average acceleration of 30.8 m/s 2, reaching a top speed of 500 km/h at the end of the course. Assuming uniformly accelerated motion, determine the time it took the dragster to reach its top speed.

Negative Acceleration Some velocity-time graphs can have a negative slope, resulting in a negative acceleration. This is generally the case when something is slowing down.

Negative Acceleration (Deceleration)

Negative Acceleration Example 1 Assuming the effects of air resistance are ignored, objects accelerate at 9.81 m/s 2 downward when they fall through the air near the earths surface. This means that if a toy car falls from the flat roof of a five-storey building, it would travel the 15-m distance in about 1.75s. Use the sign convention of down being the negative direction and up being positive to answer the next question. –If the car started from rest, determine the magnitude and direction of the car’s final velocity and 1.75s (just before striking the ground). State your answer in m/s and km/h.

Negative Acceleration Example 1 The car’s final velocity after 1.75s is 17.2 m/s down or 61.8km/h [down]

Negative Acceleration Example 1 In this situation, the car was speeding up but the acceleration was negative. Sketch a graph of the motion to help explain how it is possible to have a negative acceleration in a situation where the object is speeding up.