PHYSICS ESSENTIALS UNIT 2: MOTION

NOTE: In these notes: Vocab Log words are in RED. Words to fill-in in your notes are UNDERLINED. Some words may be both UNDERLINED and in RED.

Motion, Distance, Displacement Q: What is motion? A: Motion is any change in the position of an object. Kinematics is the study of motion (without considering the cause of the motion).

Motion, Distance, Displacement Distance vs. Displacement Distance Distance is the length an object travels along a path between two points. Metric unit for distance = meter (m)

Motion, Distance, Displacement Consists of two parts How far the object is from its starting point The direction the object traveled

Motion, Distance, Displacement Displacement is often used when giving directions Compare these two directions: walk 5 blocks vs. walk 5 blocks north. Which directions give you a better of idea of where to go?

Motion, Distance, Displacement Practice Problem #1: Think about the motion of a roller coaster car... If you measure the path along which the car has traveled, you have measured the ___________. If you consider the direction from the starting point to the car and how far the car is from where it started, you have measured the ________________. What is the car’s displacement after one complete trip around the track? ____

Motion, Distance, Displacement Displacement is an example of a vector A vector is a quantity that has magnitude and direction The magnitude can be size, length, or amount We represent vectors on a graph or map with arrows The length of the arrow is equal to the magnitude of the vector

Motion, Distance, Displacement You can add displacements using vector addition (combining vector magnitudes and directions)

Motion, Distance, Displacement For displacement along a straight line Two displacements represented by two vectors in the same direction can be added to one another (Figure A)

Motion, Distance, Displacement For two displacements in opposite directions, the magnitudes subtract from one another (Figure B)

Motion, Distance, Displacement For displacements that aren’t along a straight path For two or more displacement vectors in different directions, you can combine by graphing

Motion, Distance, Displacement The picture shows yellow vectors representing a boy’s path walking from home to school. The total distance walked is 7 blocks. The vector in red represents the boy’s total displacement. Measuring this vector gives a displacement of about 5 blocks.

Speed Q: How can we tell how fast an object is moving? A: By calculating its speed.

Speed Speed is the distance an object travels in a certain period of time Metric unit for speed = meters/second (m/s) or kilometers/hour (km/hr)

Speed We can look at speed in two ways: 1) Instantaneous Speed How fast an object is moving at any given moment in time Speed measured at a particular instant

Speed Ex: A speedometer in a car tells us instantaneous speed Ex: A radar gun used by the police to determine whether or not you are speeding while driving

Speed 2) Average Speed Average speed for the entire duration of a trip

Speed Average Speed = Total Distance Total Time OR s = d/t d s t

Speed SPEED EXAMPLE PROBLEM: John drove for 3 hours at a rate of 50 miles per hour and for 2 hours at 60 miles per hour. What was his average speed for the whole journey?

Step 1: What information are you given? Speed #1= 50 miles/hr Speed #2= 60 miles/hr Time #1= 3hours Time#2 = 2 hours Step 2: What unknown are you trying to calculate? Average speed Step 3: What formula contains the given quantities and the unknowns? Average speed = total distance total time Step 4: Replace each variable with its known value and solve. 50 mile x 3hrs = 150 miles 60 mile x 2hrs = 120 miles Hour hour Total time= 3 hours + 2 hours Average speed = 270 miles = 54 miles/hour 5 hours

Speed Practice Problem #2: While traveling on vacation, you measure the times and distances traveled. You travel 35 km in 0.4 hours, followed by 53 km in 0.6 hours. What is your average speed?

Step 1: What information are you given? Distance #1 = 35 km Distance #2 =53 km Time #1 = .4 hours Time #2 = .6 hours

Step 2: What unknown are you trying to calculate? Average speed

Step 3: What formula contains the given quantities and the unknowns? Average speed = Total Distance Total time

Step 4: Replace each variable with its known value and solve. Average speed = 35km + 53 km = 88km .4 hr + .6 hr = 1hr 88km = 88km/hr 1hr

Step 5: Does your answer seem reasonable? Could a car travel 88 km per hour? Sure, that’s about 55 miles/hr

Speed Practice Problem #3: It takes you 45 s to walk 72 m down the block to your friend’s house. What is your average speed?

Given: distance=72 m time = 45 s Average speed = total distance total time Average speed = 72m = 1.6 m/s 45 s

Graphing Speed Q: How can we visually represent the speed of an object? A: A good way to describe speed is with a distance-time graph.

Graphing Speed Graphing Constant Speed Constant Speed: When an object’s speed doesn’t change Ex: A race car with a constant speed of 96 m/s travels 96 meters every second

Graphing Speed Graph of constant speed is a straight, diagonal line

Graphing Speed When the motion of an object is graphed by plotting the distance it travels versus time, the slope of the resulting line is the object’s speed

Graphing Speed Slope = (y2-y1) (x2-x1) Choose two points on the line and plug the coordinates into the formula

Graphing Speed Practice Problem #4: draw your guess for an object moving at a slow, constant speed.

#4 Draw the actual Graph for slow constant speed here!!

#4 Pick two points and calculate slope!! Slope = Y2 – Y1 X2 – X 1 The slope will tell you the speed!!!

Graphing Speed Practice Problem #5: draw your guess for an object moving at a fast, constant speed.

#5 Draw the actual Graph for fast constant speed here!!

#5 Pick two points and calculate slope!! Slope = Y2 – Y1 X2 – X 1 The slope will tell you the speed!!!

Graphing Speed Graphing Varying Speed Varying Speed: When an object travels at different speeds during different parts of a trip Ex: A car travels 10 m/s for 60 s then travels 20 m/s for the next 120 s

Graphing Speed Slopes of the different parts of the trip can be calculated individually using the formula above Slope = (y2-y1) (x2-x1)

Varying Speed Graph

Segment #1 points (0,1) and (2,1.5) Find slope of each segment!

Segment #1 1.5-1 = 1 = .5 m/s 2-0 2 Segment #2 1.5- 1.5 = 0 = 0m/s 4-2 2 Segment #3 0-1.5 = -1.5 = -.75 m/s 6-4 2 Segment #4 2-0 = 2 = .5 m/s 10-6 4

Graphing Speed Practice Problem #6: draw your guess for an object moving slowly for 4 sec, stopping for two seconds and then moving fast for 4 sec!

#6 draw the actual graph for an object moving slowly at first, stopping for two seconds and then moving fast!

Graphing Speed Practice Problem #7: Answer the following questions about the graph to the right: 1) Which of the objects are moving at a constant speed? 2) Which object is traveling the fastest? How do you know? 3) Which object is traveling the slowest? How do you know?

All are moving at constant because they are straight lines. Cruising jet; steepesthighest slope which is the biggest number Walking person; slope closet to horizontal smallest number

Velocity Velocity is the speed AND direction in which an object is moving Velocity gives a more complete description of motion than speed alone

Velocity You solve for velocity the same way you solve for speed Speed = distance Velocity = distance & direction time time Ex: 25 km/hr Ex: 25 km/hr west

Velocity The direction of motion can be described in various ways: North, south, east, west Uphill, downhill Positive vs. negative

Velocity VELOCITY EXAMPLE PROBLEM: What is the velocity of a rocket that travels 9000 meters away from the Earth in 12.12 seconds?

Velocity Step 1: What information are you given? Distance and Direction= 9000m away from Earth Time= 12.12s Step 2: What unknown are you trying to calculate? Velocity Step 3: What formula contains the given quantities and the unknowns? v=distance time Step 4: Replace each variable with its known value and solve. v= 9000m = 742.6 m away from Earth 12.12 s s Step 5: Does your answer seem reasonable? yes

Velocity Practice Problem #8: Find the velocity of a swimmer who swims exactly 0.110 km toward the shore in 0.02 hr.

Step 1: What information are you given? Distance and Direction= .110 km toward shore Time= .02 hr

Step 2: What unknown are you trying to calculate? Velocity

Step 3: What formula contains the given quantities and the unknowns? Velocity = distance and direction time V= d/t

Step 4: Replace each variable with its known value and solve. Velocity =.110 km = 5.5km/hr toward .02 hr shore

Step 5: Does your answer seem reasonable? Yes, that’s about 8.9 miles per hour.

Velocity Practice Problem #9: Find the velocity of a baseball thrown 38 m from third base toward home plate in 1.7 s.

V=d/t V= 38m =22.4 m/s towards home 1.7s

Acceleration Q: How can we determine if there has been a change in the velocity of an object? A: By calculating the object’s acceleration.

Acceleration Acceleration is a change in velocity. Since velocity includes both speed and direction, acceleration occurs if there is a change in speed, a change in direction, or a change in both

Acceleration - Metric Unit = m/s2

Acceleration Ex: A dog chases its tail – direction is changing so the dog is accelerating Ex: A car slows down when it sees a red light – speed is changing so the car is accelerating

Acceleration Ex: A car sets its cruise control and continues to head east – the speed and direction stay the same, so the car is NOT accelerating Ex: You drop a ball off the roof of a tall building and it speeds up as it falls – speed is changing at a rate of 9.8 m/s2, so the ball is accelerating

Acceleration - Society often uses the term acceleration to describe situations in which the speed of an object is increasing.

Acceleration - Scientifically, however, the change may be an increase OR a decrease in speed Acceleration is ANY change in an object’s velocity Positive acceleration = speeding up Negative acceleration (deceleration) = slowing down

Acceleration

Acceleration In addition, an object can accelerate even if the speed remains constant Ex: Riding a bike around a curve - Although the speed remains constant, the change in direction means that you are accelerating

Acceleration This is known as uniform circular motion Ex: You can also think of a carousel The speed of the carousel remains constant throughout the ride, but the carousel is constantly changing direction This means the carousel is accelerating

Acceleration

Acceleration Constant Acceleration: A steady change in velocity of an object moving in a straight line Velocity changes by the same amount each second

Acceleration Calculating Acceleration Acceleration = a = Change in velocity = (v final – v initial) Total time t

Acceleration ACCELERATION EXAMPLE PROBLEM: A dragster in a race accelerated from stop to 60 m/s by the time it reached the finish line. The dragster moved in a straight line and traveled from the starting line to the finish line in 8.0 s.  What was the acceleration of the dragster?

Acceleration Step 1: What information are you given? Velocity final= 60 m/s Velocity initial 0m/s Time = 8.0s

Acceleration Step 2: What unknown are you trying to calculate?

Acceleration Step 3: What formula contains the given quantities and the unknowns? Acceleration = velocity final- velocity initial time

Acceleration Step 4: Replace each variable with its known value and solve. Acceleration= 60 m/s – 0 m/s = 60m/s=7.5 8.0s 8.0s Acceleration = 7.5m/s2

Acceleration Step 5: Does your answer seem reasonable? Sure

Acceleration Practice Problem #10: A ball rolls down a ramp starting from rest. After 2 seconds, its velocity is 6 m/s. What is the acceleration of the ball?

Step 1: What information are you given? Velocity final= 6m/s Velocity initial= 0m/s Time= 2 seconds

Step 2: What unknown are you trying to calculate? acceleration

Step 3: What formula contains the given quantities and the unknowns? Acceleration = velocity final- velocity initial time

Step 4: Replace each variable with its known value and solve. Acceleration= 6m/s- 0ms= 3m/s2 2s

Acceleration Practice Problem #11: A flower pot falls off a second story windowsill. The flower pot starts from rest and hits the sidewalk 1.5 s later with a velocity of 14.7 m/s. Find the average acceleration of the flower pot.

Acceleration= 14.7 ms- 0m/s = 9.8 m/s2

Graphing Acceleration You can use a speed-time graph to display and calculate acceleration The slope of a speed-time graph is equal to acceleration Speed-time graphs are linear graphs

Graphing Acceleration This graph shows positive acceleration An airplane taking off from the runway increased its speed at a constant rate because it was moving up into the sky with constant acceleration

Graphing Acceleration This graph shows negative acceleration Constant negative acceleration decreases speed Imagine a bicycle slowing to a stop The horizontal line segment represents constant speed The line segment sloping downward represents the bicycle slowing down In this case, the change in speed is negative, so the slope of the line is negative

Motion Diagrams Another way to represent acceleration and velocity is through a motion diagram. A ticker tape analysis is one way to do this. Marks are placed on a long tape at regular intervals of time.

Motion Diagrams The trail of dots gives a history of an object’s motion.

Motion Diagrams The distance between the dots represents the object’s position change during that time interval. A large distance means the object was moving fast. A small distance means the object was moving slow.

Motion Diagrams

Motion Diagrams Based on the dots on a ticker tape, we can also see if an object was moving with constant speed or accelerating.

Motion Diagrams A constant distance between dots represents constant velocity, or no acceleration. A changing distance between dots indicates changing velocity, also known as acceleration.

Motion Diagrams

Motion Diagrams We can also use “Strobe Pictures” in order to show velocity and acceleration in the same way. A camera takes a picture of an object in motion at regular intervals.

Motion Diagrams

Motion Diagrams

Motion Diagrams Vector diagrams can be used to show direction and magnitude with a vector arrow.

Motion Diagrams In a vector diagram, the size of the vector arrow tells us the magnitude . If all of the arrows are the same length, then the magnitude is constant. In the case of a moving car, this would mean that the velocity of the car is constant while it is moving.

Motion Diagrams If the size of the arrows increase or decrease, this would mean that the car is changing velocity or accelerating.