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Graphing Speed & Acceleration

Graphing Speed & Acceleration. Making and Interpreting Distance – Time Graphs. GRAPHING SPEED DISTANCE-TIME GRAPHS. Distance is plotted on the vertical axis. D I S T A N C E. Time is plotted on the horizontal axis. TIME. CONSTANT SPEED.

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Graphing Speed & Acceleration

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  1. Graphing Speed & Acceleration Making and Interpreting Distance – Time Graphs

  2. GRAPHING SPEEDDISTANCE-TIME GRAPHS Distance is plotted on the vertical axis. D I S T A N C E Time is plotted on the horizontal axis. TIME

  3. CONSTANT SPEED • If something is “constant” what does that mean? • It does not change • What does the term constant speed mean? • Speed that does not change is constant speed. • Name some things that you think have constant speed.

  4. GRAPHING CONSTANT SPEEDDISTANCE-TIME GRAPHS straight diagonal line t d 100 90 80 70 60 50 40 30 20 10 1 2 3 4 5 20 40 60 80 100 D I S T A N C E (m) 0 1 2 3 4 5 TIME (sec) Describe the shape of the line for constant speed

  5. GRAPHING CONSTANT SPEED DISTANCE-TIME GRAPHS A has the > slope therefore it has the > constant speed. How do you know? A B C t d 100 90 80 70 60 50 40 30 20 10 1 2 3 4 5 20 40 60 80 100 D I S T A N C E (m) 0 1 2 3 4 5 TIME (sec) Which object has the greatest constant speed?

  6. GRAPHING AVERAGE SPEED DISTANCE-TIME GRAPHS A flat horizontal line means motion stopped. What does this part of the line mean? 100 90 80 70 60 50 40 30 20 10 t d 1 2 3 4 5 10 30 40 40 80 D I S T A N C E (m) 0 1 2 3 4 5 zigzag TIME (sec) Describe the shape of the line for average speed?

  7. Average Speed • Average speed is speed that changes or fluctuates. • Most moving objects travel at average speed, • they start from a stand still, begin slowly, increase their speed, slow down, speed up, and eventually slow to a stop. • On a distance-time graph average speed would appear as a line that changes direction as it goes across the graph. It would be described as a zig-zag line. • A slanted line indicates that motion is occurring. • A flat horizontal line indicates that motion has stopped but time continues.

  8. Review • You will recall from a previous lesson that Speed is calculated using the formula • s = d / t • What is the average speed of a 18 wheeler driver who drives non-stop 1600 miles from Houston to Los Angeles in 23 hours? • S = d / t • S = 1600 mi / 23 hrs. • S = 69.565 mi/hr.

  9. Acceleration • In order to understand acceleration you must understand the difference in speed and velocity. • Speed is how long it takes a moving object to travel a distance. • Velocity is speed in a given direction. • NOW, ACCELERATION IS THE RATE OF CHANGE IN VELOCITY. • You must understand that if either speed or direction changes, the object has undergone acceleration.

  10. In this diagram, how many times will the people experience acceleration from where they are now to the end of the ride? 1 Speeds up 2 ??? Speeds up Is there any other place that its velocity will change? Slowing down is also considered to be acceleration. Let’s look at why this might be.

  11. Formula for CALCULATING ACCELERATION • acc = final velocity - original velocity time for change to occur acc = Vf - Vo t • At the top of the hill the roller coaster is moving 20 m/sec and increases in speed to 40 m/sec at the bottom of the hill. It takes 4 seconds to reach the bottom of the hill. • What is the roller’s coaster’s acceleration? • acc= Vf_-_Vo t 40 m/s__-__20 m/s 4 sec acc = 5 m/s/s

  12. As it goes up the hill, it slows to 20 m/sec. The total time from the bottom of the hill to the top of the next hill is 5 seconds. What is the acceleration of the roller coaster? • acc = Vf__- Vo t acc = 20 m/s_-_40 m/s 5 seconds acc = - 4 m/s/s

  13. GRAPHING ACCELERTION DISTANCE-TIME GRAPHS 100 90 80 70 60 50 40 30 20 10 t d 1 2 3 4 5 10 20 40 70 110 D I S T A N C E (m) CURVED 0 1 2 3 4 5 TIME (sec) Describe the shape of a line showing acceleration.

  14. FIRST ANNUAL D C B A CNE Snail Races

  15. CNE INTERPRETING DISTANCE-TIME GRAPHS SNAIL RACES Results a c 100 90 80 70 60 50 40 30 20 10 b D I S T A N C E (in) d Pass out question sheet for this slide. 0 1 2 3 4 5 TIME (hr)

  16. INTERPRETING A DISTANCE-TIME GRAPH Questions • What kind of graph is this? • Snail _____was fastest at the beginning of the race. • The slowest at the beginning was snail ______. • Which snail stopped during the race?______ • How long was it stopped? • How far had snail A gone after 2 hours? • Snail_____ got faster and faster as the race went on. • After 4 hours Snail B had gone _____inches. • It took snail C _____hours to cover 50 inches. • Snails ____&____ traveled at constant speed. • Snail_____ had the fastest constant speed. • What was the average speed of snail C? • (show your work below)

  17. INTERPRETING A DISTANCE-TIME GRAPH Questions Distance time graph • What kind of graph is this? • Snail _____was fastest at the beginning of the race. • The slowest at the beginning was snail ______. • Which snail stopped during the race?______ • How long was it stopped? • How far had snail A gone after 2 hours? • Snail_____ got faster and faster as the race went on. • After 4 hours Snail B had gone _____inches. • It took snail C _____hours to cover 50 inches. • Snails ____&____ traveled at constant speed. • Snail_____ had the fastest constant speed. • What was the average speed of snail C? • (show your work below) C D C 2 hours 49-50 in D ~65 4 A B A BONUS: Which snail won the race? (5 pts) S = d / t S = 100 in / 5 hr S = 20 in / hr Me, snail A A

  18. Model Car Races Time Total distance covered (meters) Construct a distance – time graph for the values in the data table. PASS OUT GRAPH PAPER FOR THIS EXERCISE.

  19. Model Car Race Results Graphed D I S T A N C E (m) TIME (sec) Your graph should look like this.

  20. A few questions for you: • What does the horizontal line for car C indicate? • Which car(s) is/are accelerating? How do you know? • Which car(s) is/are traveling at constant speed? • Which car won the race? • How do you know which car won the race? • What is the average speed of each car in the race?

  21. A few questions for you: • What does the horizontal line for car C indicate? • Which car(s) is/are accelerating? How do you know? • Which car(s) is/are traveling at constant speed? • Which car won the race? • How do you know which car won the race? • What is the average speed of each car in the race? It had to stop during a portion of the race Car D because its line is curving. Cars A and B show straight diagonal lines Car D because it traveled farther in the 10 seconds Because it traveled farther in the 10 seconds A 3 m/sB 2 m/sC 2.5 m/sD 3.6 m/s

  22. Quiz • 1.The graph used to graph speed is called a ___________-______ graph. • 2. Speed that does not change is called ____________ speed. • 3. Speed that fluctuates is called _______________ speed. • 4. The shape of a line on a distance-time graph for constant speed is a ________________, _______________ line. • 5. The > the slope the _______ the constant speed. • 6. On a distance time graph a line that is horizontal indicates ___________________ ______________. • 7. The formula for calculating speed is _________=__________ • 8. Speed in a given direction is called _________________. • 9. The rate of change in velocity is called___________________.

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