Speed, Acceleration and Momentum

1. Speed, Acceleration and Momentum Forces in Motion Mrs. Jeffries

2. Motion and Point of Reference • Motion is a change in position • Determining whether or not something has changed its position depends on your Point of Reference. • Your point of reference is where you are relative to the moving object.

3. Speed Speed is the rate that indicates how much distance you traveled divided by the amount of time that you traveled. It is measured in meters per second (m/s). Formula = distance (meters) time (seconds) Example: You ran the 100 m dash in 20 seconds 100 m 20 s = 5 m/s (you traveled 5 meters every second you were running)

4. Velocity • Velocity is the exact same formula as speed, but it has one big difference. VELOCITY IS THE SPEED PLUS THE DIRECTION YOU ARE TRAVELING. • Use the example from before: You ran the 100 m dash in 20 seconds 100 m 20 s = 5 m/s W (you traveled 5 meter per second in a western direction)

5. Average Speed vs. Constant Speed • Most of the time we calculate average speed (example: going to Grandma’s house). • However, in some cases, an object travels at a constant rate when the speed never changes (do you have cruise control on your car?)

6. Average Speed Graph

7. Graphing Average Speed • Suppose Grandma lived 240 miles away, and you traveled there in 4 hours. Your car probably traveled at different velocities (different speeds at different directions), and you may have made a few stops along the way. So your graph would not be a perfectly straight line.

8. Constant Speed • Let’s say that the road to Grandma’s was a straight line, and there were no stops or delays along the way. If you traveled at a constant speed of 60 mph, then a constant speed would be graphed as a straight line.

9. Graphing Constant Speed

10. Acceleration • Most people think of acceleration as speeding up, but acceleration is actually a change in velocity over time. Formula: Final Velocity – Starting Velocity Time (sec) = m/s2 Or m/s/s

11. Acceleration • Acceleration can occur when • You are increasing your speed (positive acceleration) • You are decreasing your speed (negative acceleration or deceleration) • You are changing direction

12. Acceleration Problems • You start off riding your bike at 5 m/s. Then you go down a big hill. At the bottom of the hill your are traveling at 15 m/s. It took you 5 seconds to go from the top of the hill to the bottom of the hill • 1) What was your rate of acceleration? • 2) Was it positive or negative acceleration?

13. Acceleration Problems • You are riding your bike at 20 m/s. You now are having to go uphill. You don’t exert more effort, so, by the time you reach the top of the hill, you are traveling at 10 m/s. It took you 10 seconds to go from the bottom of the hill to the top. • 1) Is this positive or negative acceleration? • 2) what was your rate of acceleration?

14. Momentum • Momentumis really a measure of how difficult it is to stop a moving object. • An object that collides with an object at rest (and bounces off )will have the same momentum as it had before. • An object that collides with an object in motion will experience a momentum that is a combination of both moving objects.

15. Momentum Formulas • Momentum equals the mass of an object times its velocity: p (momentum) = mv • So an 20 kg object traveling at 100 m/s W: P(force) = 20 kg x 100 m/s west = 2000kg/m/s west If p = m x v, How would you find either mass or velocity (if you had force?) You would divide either into the force (P) M = p/v or V = p/m

16. Inertia Newton’s First Law of Motion proves that objects do not move or stop moving unless there are greater (unbalanced) forces acting upon them. This is what inertia is. Inertia is the object’s tendency to either keep moving or not moving at all. A force that changes this has to be strong enough to change an object’s inertia.

17. Can You Solve These Problems? Look at the formulas and solve the following problems on speed, acceleration or momentum. Be sure to write down the formula first, plug in the numbers, and always write the ending units. You may want to underline or highlight the numbers in the problems.

18. Speed The Jones family traveled north to New York. The family traveled a total of 480 miles in 12 hours. What was their average speed? Myra is the school’s fastest runner. In her last race she ran for 10 seconds, and her average speed was 6 m/s. How far did she run?

19. Speed Problems 1) 480 miles 12 hours = 40 miles/hr 2) Plug in the numbers you know: _ ?___ 6 m/s = 10 s (What does 10 go into 6 times?) 60 m 6 m/s = 10 s Does it work? Answer: 60 m

20. Acceleration Problems 3) Sam rode brother ‘s Big Wheel He started off traveling at 2 m/s. By the time Sam broke the toy, he had traveled for 4 s at 10 m/s. What was Sam’s rate of acceleration? 4) A train arrives at a station traveling at 10 miles per hour. 30 minutes ago it was traveling at 40 miles per hour. What was the train’s rate of acceleration?

21. Acceleration Problems 10 m/s – 2 m/s8 m/s 4 s = 4 s = 2 m/s/s ( or 2 m/s2) 4) Plug in what you know: 10 mph – 40 mph-30 mph 30 minutes = 30 minutes = -1/m/hr/minute

22. Acceleration Problem 5) An airplane’s rate of acceleration is 50 m/s2. The starting speed was 100 m/s. After a while the plane was traveling at 200 m/s. How long did it take the plane to accelerate?

23. Plug in What You Know 200 m/s – 100 m/s 50 m/s2 = ? Solve the first line: 100 m/s 50 m/s2 = ? What goes into 100 50 times? 2! 100 m/s 50 m/s2 = 2 s Does it work?

24. Momentum Problems 6) An object with a mass of 50 kg is traveling at 14 m/s east. What is the force of this object? 7) An object thrown from a bridge has a force of 500g/m/s down. It has a mass of 125 g. What is the velocity of this object?

25. Plug It In! P = m x v, so p = 50 kg x 14 m/s east p = 700 kg/m/s east 500 g/m/s down = 125 g x ? How many times does 125 go into 500? 4! 500 g/m/s down = 125 g x 4 m/s downDoes it work?