Velocity time graphs

1. Velocity time graphs

2. Goals for today • Discuss V-T graphs • Homework • In the books p 338-339 proms 2-7, 10-11, 14-16, 22-28 -- Graph handout Test for honors is Wednesday CP is Thursday

3. Differences between V-t graphs and P-T graphs • The vertical #’s tell how fast, not location • V-t does not indicate start position • Direction is indicated by position on graph, not slope • Acceleration is indicated differently on each type of graph

4. Horizontal lines on a V-T graph Velocity (m/s) Time (s)

5. Can you mimic the graph Using the motion detector

6. Tilted lines on V-T graphs V (m/s) T (m/s)

7. What do tilted lines mean on a V-T graph? • The object is changing its velocity • Acceleration • How it accelerates is determined by • Location of graph (Above, Below x-axis) • Type of tilt

8. Acceleration is… • A change in the velocity of the object • Tilted lines on a V-T graph indicate acceleration • Acceleration can be calculated by finding the slope value of these lines

9. Tilted lines on V-T graphs V (m/s) T (m/s)

10. What kind of motion is indicated on this graph? V (m/s) T (s)

11. What would curves mean on a V-T graph • Curves would indicate non-constant acceleration • Think roller coaster rides, when you get pushed against the harness or back into the seat • The ‘Jerk’

12. Identify motion for each part of the V-T graph V (m/s) T (m/s)

13. Identify motion for each part of the V-T graph V (m/s) T (m/s)

14. Create a V-t graph that… • Section 1: Shows constant motion of (-3) m/s for 5 seconds. • Section 2: Shows constant acceleration (slowing down in the negative direction) • Section 3: Shows no movement for 5 seconds • Section 4: Shows constant acceleration (speeding up in the positive direction)

15. Answer

16. Homework • For all graphs: • Find the direction • Constant Velocity or Non-Constant Velocity • Fast, Average or Slow • Faster, Slower (Change in Velocity)

17. Finding overall displacement from V-T graph • How far does an object travel if it goes 3 m/s for 10 seconds? V 3 t 10

18. Acceleration • Anytime the velocity of an object changes, the object accelerates • Getting Faster • Getting Slower • If the motion of object changes direction going the same speed

19. Speeding up Slowing down Velocity changes if…

20. Velocity changes if… • The direction of the motion changes, but the speed does not • This type of acceleration is call centripetal acceleration

21. Equation for average acceleration a = (vf - vi) / t vf = final velocity vi = initial velocity t = elapsed time a = acceleration

22. Ex #1 • A flowerpot falls off a second story windowsill. The flowerpot start from rest and hits the sidewalk 1.5 s later with a velocity of 14.7m/s. Find the average acceleration.

23. What information is given?Identify the information. • 1.5s • Is the time • 14.7 m/s • is the final velocity • Starts from rest • Means that the initial velocity is zero (0) • “at rest” always means that vi = o

24. Answer #1 • a = (14.7 – 0) / 1.5 = 9.8 • What are the units? • (14.7 m/s – 0 m/s) 1.5 s = (m/s) / s • m / s2

25. Ex #2 • While driving at an average velocity of 15.6 m/s down the road, a driver slams on brakes to avoid hitting a squirrel. The car stops completely in 4.2 seconds. What is the acceleration of the car?

26. Givens 15.6 m/s = vi 4.2 s = t 0 = vf • What you want to solve for acceleration

27. Solution a = (0 – 15.6) / 4.2 = (-3.7) m/s2

28. Questions on homework in book • Pg 324 • Pg 328

29. Mr. Baker’s Monster problem • On a dark and scary night, Mr. Baker was walking down the street at 5.234 m/s. He heard a horrible sound of hundreds of shuffling feet behind him and increased his speed to a new 78.985 m/s. What was the amount of time (in minutes) needed to increase his speed, if his rate of acceleration was 1.9 m/s2 ?

30. Answer Given: vi = 5.234 m/s a = 1.9 m/s2 vf = 78.985 m/s Want: time (in minutes) a = (vf – vi) / t 1.9 = (78.985 -5.234) / t