MOTION, DISTANCE, AND DISPLACEMENT Q: What is motion? A: Motion is any change in the position or place of an object. is the study of motion (without

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1 MOTION, DISTANCE, AND DISPLACEMENT Q: What is motion? A: Motion is any change in the position or place of an object. is the study of motion (without considering the cause of the motion). Distance vs. Displacement - Distance - Distance is the length an object travels along a path between two points. - Metric unit for distance = - Displacement - Displacement consists of two parts 1) How far the object is from its starting point 2) The - 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? Practice Problem #1: Think about the motion of a roller coaster car... 1) If you measure the path along which the car has traveled, you have measured the. 2) 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. 3) What is the car s displacement after one complete trip around the track? - Displacement is an example of a vector - A vector is a quantity that has and - 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 - You can add displacements using vector addition (combining vector magnitudes and directions) - For displacement along a straight line: Two displacements represented by two vectors in the same direction can be to one another (Figure A) 1

2 For two displacements in opposite directions, the magnitudes from one another (Figure B) - For displacements that aren t along a straight path For two or more displacement vectors in different directions, you can combine by graphing The picture shows yellow vectors representing a boy s path walking from home to school. The total distance walked is blocks. The vector in red represents the boy s total displacement. Measuring this vector gives a displacement of about blocks. SPEED Q: How can we tell how fast an object is moving? A: By calculating its 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) - We can look at speed in two ways: 1) How fast an object is moving at any given moment in time Speed measured at a particular instant 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 2

3 2) Average speed for the entire duration of a trip d Average speed = Total Distance Total Time s t OR s = d/t 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? Step 2: What unknown are you trying to calculate? Step 3: What formula contains the given quantities and the unknowns? Step 4: Replace each variable with its known value and solve. Step 5: Does your answer seem reasonable? 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? 3

4 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? 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 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 - Graph of constant speed is a straight, diagonal line - When the motion of an object is graphed by plotting the distance it travels versus time, the of the resulting line is the object s Slope = (y 2 -y 1 ) Choose two points on the line and plug the (x 2 -x 1 ) coordinates into the formula Practice Problem #4: Draw a distance(position) time graph for a person walking a constant SLOW speed. Draw your guess 4

5 Observe the demonstration and draw the ACTUAL GRAPH of a person walking slowly below: Practice Problem #5: Draw a distance(position) time graph for a person walking a constant FAST speed. Draw your guess 5

6 Observe the demonstration and draw the ACTUAL GRAPH of a person walking quickly below: - 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 - Slopes of the different parts of the trip can be calculated individually using the formula above 6

7 Practice Problem #6: Draw a distance-time graph of an object traveling at a constant slow speed for 4 seconds, stopping for 2 seconds, then traveling at a constant fast speed for 4 seconds. Observe the demonstration and then draw the actual graph below: 7

8 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? VELOCITY - Velocity is the in which an object is moving - Velocity gives a more complete description of motion than speed alone - 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 - The direction of motion can be described in various ways: North, south, east, west Positive vs. negative VELOCITY EXAMPLE PROBLEM: What is the velocity of a rocket that travels 9000 meters away from the Earth in seconds? Step 1: What information are you given? Step 2: What unknown are you trying to calculate? 8

9 Step 3: What formula contains the given quantities and the unknowns? Step 4: Replace each variable with its known value and solve. Step 5: Does your answer seem reasonable? Practice Problem #8: Find the velocity of a swimmer who swims exactly km toward the shore in 0.02 hr. Practice Problem #9: Find the velocity of a baseball thrown 38 m from third base toward home plate in 1.7 s. 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 is a - 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 - Metric unit = Ex: A dog chases its tail direction is changing so the dog is accelerating 9

10 Ex: A car slows down when it sees a red light speed is changing so the car is accelerating 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/s 2, so the ball is accelerating - Society often uses the term acceleration to describe situations in which the speed of an object is increasing - Scientifically, however, the change may be an increase OR a decrease in speed Acceleration is Positive acceleration = speeding up Negative acceleration (deceleration) = - In addition, an object can accelerate even if the speed remains Ex: Riding a bike around a curve o Although the speed remains constant, the change in direction means that you are accelerating o This is known as Ex: You can also think of a carousel o The speed of the carousel remains constant throughout the ride, but the carousel is constantly changing direction o This means the carousel is - Constant Acceleration: A steady change in velocity of an object moving in a straight line Velocity changes by the same amount each second - Calculating Acceleration Acceleration = a = Change in velocity = (v final v initial ) Total time t 10

11 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? Step 1: What information are you given? Step 2: What unknown are you trying to calculate? Step 3: What formula contains the given quantities and the unknowns? Step 4: Replace each variable with its known value and solve. Step 5: Does your answer seem reasonable? 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? 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. 11

12 GRAPHING ACCELERATION - You can use a to display and calculate acceleration - The slope of a velocity-time graph is equal to - Velocity-time graphs are linear graphs 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 This graph shows negative acceleration Constant negative acceleration decreases speed Imagine a bicycle slowing to a stop The horizontal line segment represents 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 - Another way to represent acceleration and velocity is through a A ticker tape analysis is one way to do this Marks are placed on a long tape at regular intervals of time The trail of dots gives a history of an 12

13 The distance between the dots represent the object s position change during that time interval o A large distance means the object was moving o A small distance means the object was moving Based on the dots on a ticker tape, we can also see if an object was moving with constant velocity or accelerating o A constant distance between dots represents, or no acceleration o A changing distance between dots indicates changing velocity, also known as - We can also use strobe pictures in order to show velocity and acceleration in the same way A camera take a picture of an object in motion at regular intervals 13

14 - Vector diagrams can be used to show direction and magnitude with a vector arrow In a vector diagram, the size of the vector arrow tells us the o If all of the arrows are the same length, then the magnitude is o In the case of a moving car, this would mean that the velocity of the car is constant while it is moving o If the size of the arrows increase or decrease, this would mean that the car is changing velocity, or accelerating 14