1. Velocity, Acceleration & Free Fall
Chapter 2
Velocity, Acceleration & Free Fall

2. Displacement Displacement – change in location ∆x = x2 – x1
Displacement ≠ Distance traveled

3. Are you moving???? Compared to what??????
Surface of earth; axis of earth; sun; milky way
All depends on your frame of reference

4. Velocity – a Vector
2-part - magnitude (speed) and direction

5. Instantaneous vs. Average Velocity
Instantaneous - the speed at any instant – Speedometer
average - Total distance covered/Total time

6. Velocity calculations
Velocity = Δdistance/Δtime
Units – distance per time - m/s
distance = velocity*time

7. Check Problems
On May 29, 1988, Rick Mears won the Indianapolis 500 in 3.45 hr. What was his average speed (in mi/hr and m/s)?
The slowest animal ever discovered was a crab found in the red sea. It traveled with an average speed of 5.70 km/yr. How long would it take this crab to travel 100 km? What is its speed in m/hr?

8. Check problems (cont.)
Hans stands at the rim of the Grand Canyon and yodels down to the bottom. He hears his yodel echo back from the canyon floor 5.20 s later. Assume that the speed of sound in air is 340 m/s. How deep is the canyon at this location?
On July 2, 1988, Steve Cram of Great Britain ran a mile in 3.81 min. During this amazing run, what was his average speed in a mile/min? Mile/hr? m/s?

9. Constant Velocity vs. Changing Velocity
Can you feel a change in velocity?
Speeding up - gas pedal
Slowing down - brake
Turning - steering wheel
Constant speed and constant direction

10. Graphing – relationship between distance & velocity
Distance vs. Time graphs
Velocity vs. Time graphs

11. Velocity Velocity – rate at which distance is covered
Velocity*Time = Distance; vt = d
Slope of d vs. t graph is velocity

12. Acceleration - defined
Acceleration – rate of change of velocity
Acceleration = Δvelocity/Δtime
How fast you are going faster, slower, or turning

13. Acceleration simple examples
A Cheetah increases its velocity from 15 m/s to 30. m/s in 2.0 seconds. What is its acceleration?
A Bugatti Veyron can go from rest to 60. miles per hour in 3.0 seconds. What is its acceleration?
Cruising along at 50.0 km/hr you see a red light and brake to a stop in 4.00 seconds. What is your acceleration?

14. Instantaneous vs. Average
At an instant – slope from V vs. t graph
Average – total Δv/ total Δt

15. Graphical relationships
D vs. t – slope is velocity
V vs. t – slope is acceleration, area under the curve is distance traveled
A vs. t – slope is jerk, area under the curve is final velocity

16. Constant acceleration
Initial velocity + acceleration*time = final velocity
vi + at = vf
Simply add product of acceleration and time it is applied to initial velocity
A lion is trotting along at 5 m/s when it sees a zebra. It accelerates at a constant rate of 4 m/s/s for 3 seconds. What is its final speed.

17. Finding distance - constant acceleration
Find average velocity: vavg = (vi + vf)/2
Distance = vavg*time
Together d = ½(vi + vf)*t
A train leaves the station with a velocity of 12 m/s. 3 seconds later it has a velocity of 36 m/s. How far has it traveled (assuming constant acceleration)?

18. Const. Acc. equation summary
vf = vi + at don’t know d
d = ½(vi + vf)*t - don’t know a
d = vit + ½at don’t know vf
5 variables, given 3, choose the right equation and solve for desired 1

19. Gravity – example of const. acc.
Earth’s gravitational force produces an acceleration on all masses
Gravitational acceleration (g) = 9.8 m/s2
Constant around surface of the earth
Tennisball - graph

20. Gravity examples
Use constant acc. Equations with g for your acceleration
How fast is a skydiver going after 4.00 seconds?
How far has a skydiver gone in 5.00 seconds?
How long will it take a skydiver to fall kilometer?

21. Problem Solving Strategy
Read problem – get a sense of what is going on – sketch it if that is helpful
Identify what quantities are given
Identify what is being asked for
Find the right equation and check that it can be used
Rewrite equation to solve for desired quantity
Substitute values into equation to get answer
Check that answer has right units and makes sense