Motion

Motion Change in position with respect to change in time

Position The separation from the origin

Position & Time

Position-Time Graph

Position-Time Graph (2)

Average Velocity Average velocity is the change in position (displacement) divided by the time interval during which the displacement took place. If you know two of the three quantities in this relationship, you can determine the third mathematically.

Average Velocity 1. A car travels at 55 km/h for 6.0 hours. How far does it travel? 2. A missile travels 2500 km in 2.2 hours. What is its velocity? 3. How many minutes will it take a runner to finish an 11-km race at 18 km/h?

Average Velocity 5. A businesswoman on a trip flies a total of 23,000 km. The first day she traveled 4000 km, the second day 11,000 km, and on the final day she was on a plane that could travel at 570 km/h. How long was she on the plane the final day?

Instantaneous Velocity The velocity at a single point in time.

Instantaneous Velocity 1. Many cars require an oil change every 4000–5000 km. If this car travels without a break for 4800 km at 120 km/h, how long will it take to simulate one full cycle of time without an oil change? 2. Some cars have a warranty that lasts for up to 150,000 km. How long would it take for the warranty to run out if the car ran constantly at 110 km/h?

Instantaneous Velocity 3. A car is tested for 1800 km on one day, 2100 km another day, and then is driven 65 km/h for 72 hours. What is the total distance the car has traveled? 4. The odometer on a car reads 4100 km after 3 days of tests. If the car had been tested on one day for 1500 km, a second day for 1200 km, then how long was the car tested the last day if it traveled at 120 km/h while being tested?

Instantaneous Velocity 5. Car A traveled 1200 km in 8.0 h. Car B traveled 1100 km in 6.5 h. Car C traveled 1300 km in 8.3 h. Which car had the highest average velocity. How long would it have taken the slowest car to travel the same distance as the fastest car? 6. One car tested can travel 780 km on a tank of gasoline. How long should the car be able to travel at 65 km/h before it runs out of gas? If the car has a 53-L tank, then what is the average mileage of the vehicle?

Instantaneous Velocity 7. Cars Q and Z are put through an endurance test to see if they can travel at 120 km/h for 5.0 hours. Each car has a 45-L fuel tank. Car Z must stop to refuel after traveling for 4.2 hours. Car Q, however, travels for 5.4 hours before running out of gas. For each car, calculate the average kilometers traveled for each liter of gas (km/L).

Instantaneous Velocity 8. Refer to the problem above. How many liters does Car Q have left in its fuel tank after traveling for five hours at 120 km/h? If you were to test-drive Car Q across a desert where there were no fuel stations available for 1200 km, how many 10-L gas cans should you have in the car to refuel along the way?

Motion Diagram

Vector A quantity that has both magnitude and direction 3m South (-3y) Scalar A quantity that has only magnitude 3m

Velocity vs. Speed Velocity: Total displacement (change in position) with respect to total time Speed Total distance traveled with respect to total time

Motion Diagram

Vector Addition

Vector Addition

Vector Subtraction

Vector Addition Tail to Tip

Vector Addition Total distance = 7m Time elapsed = 7s X = 4m Y = 3m Total displacement = sqrt(4^2 + 3^2)=5m (a^2+b^2=c^2) y 3 2 Velocity = 5m/7s = 0.7m/s Speed = 7m/7s = 1m/s 1 x 1 2 3 4 (one second per block)

Practice Problem Joe goes for a run. From his house, he jogs north for exactly 5.00h at an average speed of 10.0 km/h. He continues north at a speed of 10.0 km/h for the next 30.0h. He then turns around and jogs south at a speed of 15.0 km/h for 15.0h. Then he jogs south for another 20.0h at 5.00 km/h. He walks the rest of the way home. How many kilometers does Joe jog in total? How far will Joe have to walk to get home after he finishes jogging?

Practice 1. An airplane travels at a constant speed, relative to the ground, of 900.0 km/h. a. How far has the airplane traveled after 2.0 h in the air? b. How long does it take for the airplane to travel between City A and City B if the cities are 3240 km apart? c. If a second plane leaves 1 h after the first, and travels at 1200 km/h, which flight will arrive at City B first? 2. You and your friend start jogging around a 2.00x10^3-m running track at the same time. Your average running speed is 3.15 m/s, while your friend runs at 3.36 m/s. How long does your friend wait for you at the finish line?

Practice 3. The graph shows the distance versus time for two cars traveling on a straight highway. a. What can you determine about the relative direction of travel of the cars? b. At what time do they pass one another? c. Which car is traveling faster? Explain. d. What is the speed of the slower car?

Practice 4. You drop a ball from a height of 2.0 m. It falls to the floor, bounces straight upward 1.3 m, falls to the floor again, and bounces 0.7 m. a. Use vector arrows to show the motion of the ball. b. At the top of the second bounce, what is the total distance that the ball has traveled? c. At the top of the second bounce, what is the ball’s displacement from its starting point? d. At the top of the second bounce, what is the ball’s displacement from the floor?

Practice 5. You are making a map of some of your favorite locations in town. The streets run north–south and east–west and the blocks are exactly 200 m long. As you map the locations, you walk three blocks north, four blocks east, one block north, one block west, and four blocks south. a. Draw a diagram to show your route. b. What is the total distance that you traveled while making the map? c. Use your diagram to determine your final displacement from your starting point. d. What vector will you follow to return to your starting point?

Practice 6. An antelope can run 90.0 km/h. A cheetah can run 117 km/h for short distances. The cheetah, however, can maintain this speed only for 30.0 s before giving up the chase. a. Can an antelope with a 150.0-m lead outrun a cheetah? b. What is the closest that the antelope can allow a cheetah to approach and remain likely to escape?

Practice 7. The position-time graph to the right represents the motion of three people in an airport moving toward the same departure gate. a. Which person travels the farthest during the period shown? b. Which person travels fastest by riding a motorized cart? How can you tell? c. Which person starts closest to the departure gate? d. Which person appears to be going to the wrong gate?

Practice 8. A radio signal takes 1.28 s to travel from a transmitter on the Moon to the surface of Earth. The radio waves travel at 3.00x10^8 m/s. What is the distance, in kilometers, from the Moon to Earth?

Practice 9. You start to walk toward your house eastward at a constant speed of 5.0 km/h. At the same time, your sister leaves your house, driving westward at a constant speed of 30.0 km/h. The total distance from your starting point to the house is 3.5 km. a. Draw a position-time graph that shows both your motion and your sister’s motion. b. From the graph, determine how long you travel before you meet your sister. c. How far do you travel in that time?

Practice 10. A bus travels on a northbound street for 20.0 s at a constant velocity of 10.0 m/s. After stopping for 20.0 s, it travels at a constant velocity of 15.0 m/s for 30.0 s to the next stop, where it remains for 15.0 s. For the next 15.0 s, the bus continues north at 15.0 m/s. a. Construct a d-t graph of the motion of the bus. b. What is the total distance traveled? c. What is the average velocity of the bus for this period?

Position vs. Time

Review 2.1 1. What is a motion diagram? A series of images showing the position of a moving object at equal time intervals. 2. How is a particle diagram different from a motion diagram? Which diagram is simpler? The particle model is a motion diagram in which the object has been replaced by a series of single points. The particle model is simpler than the motion diagram. 3. What are the two components used to define motion? Place and time 4. Give three examples of straight-line motion. Car, meteor, light

Review 2.2 1. What is the primary difference between a scalar and a vector? A vector has both magnitude and direction, while a scalar only has magnitude. 2. What is a resultant? A resultant is the sum of two or more vectors. 3. A student walks 4 blocks north then stops for a rest. She then walks 9 more blocks north and rests, then finally another 6 blocks north. What is her displacement in blocks? Δd = df- di If the student’s starting point is defined as zero, the equation becomes Δd = df. Thus, the student’s displacement is equal to his or her final position and the final position is equal to the sum of all of the displacements. So, Δd = d1+d2+d3 Δd = (4 blocks N)+(9 blocks N)+(6 blocks N) = 19 blocks N

Review 2.2 4. A runner runs 6 km east, 6 km north, 6 km west, and finally 6 km south. What is his total displacement? Draw a diagram. 6 km West 6 km South 6 km North Starting Point 6 km East

Review 2.3 1. On a position-time graph, which of the two variables is on the x-axis? Which is on the y-axis? Time is represented on the x-axis and position is represented on the y-axis. 2. If the plotted line on a position-time graph is horizontal what does this indicate? The object the graph represents is not moving. 3. Can the plotted line on a position-time graph ever be vertical? Explain your answer. This is unlikely, as this would represent an object moving at an infinite speed.

Review 2.3 4. A position-time graph plots the course of two runners in a race. Their lines cross on the graph. What does this tell you about the runners? They are in the same place at the same time. 5. Does the intersecting line on a position-time graph mean that the two objects are in collision? Explain The objects are in the same place at the same time, but they are not necessarily in collision. All that is known is that their position with reference to the origin is the same.

Review 2.4 1. What is the difference between speed and velocity? Speed does not contain a direction component and velocity does. In other words, speed is a scalar quantity and velocity is avector quantity. 2. What is the difference between average velocity and instantaneous velocity? Give an example of each. Average velocity is the total distance traveled divided by the total time of travel. An example of average velocity is a 120-mile car trip that takes 2 hours, average velocity was 60 mph. Instantaneous velocity is the velocity at one given instant. An example of instantaneous velocity is the velocity recorded by a police radar gun. 3. Define all three variables in the equation v=Δd/Δt and indicate the appropriate label for each in SI terms. v is velocity in m/s, t is time in s, d is distance in m.

Review 2.4 4. What is the average velocity of a car that travels 450 km in 9.0 hours? v=Δd/Δt 450km/9.0h = 5.0x10^1 5. How far has a cyclist traveled if she has been moving at 30 m/s for 5.0 minutes? Δd=vΔt (30m/s)(3.0x10^2 s) = 9000m

Velocity vs. Time (Ch 3)