1. One-Dimensional Motion
Introduction to Displacement and Velocity

2. Objectives Define and calculate displacement
Differentiate between displacement and distance
Solve velocity problems
Differentiate between velocity and speed

3. Displacement
Straight-line distance between the initial and final points
Has direction and magnitude
Δx, xf-xi
X represents position
Can be positive or negative
Measured in ft, m, km, etc

4. Distance Not the same as displacement Only has magnitude, no direction
Always greater than
or equal to
displacement

5. Examples If I walk 2 m east, what is my displacement?
If walk 2 m east and 2 m west, what is my displacement?
Graph
2 m east
The graph should have distance on the y axis, above the x axis is the right, below the x axis is on the left

6. Vectors Vs Scalars
Vectors- Quantities that have magnitude and direction
Scalars-quantities that only have magnitude
Resultant- vectors added together
bbb

7. Velocity Change of position of an object over an interval of time
V=Δx/Δt = xf-xi/t f-t I
Has magnitude and direction
Vector or scalar?
VECTOR!

8. Example
Ms. K takes her dog Zeus for a walk. If they walk for 27 min and travel 1.89 km east, what is their average velocity in meters/sec?
1.2 m/s east

9. Speed The change in distance over an interval of time
Speed=Δx/Δt= xf-xi/t f-t I
Only has magnitude no direction!
Vector or scalar?
They are the same only when moving in a straight line
Scalar

10. Example 1
Polar Bears are extremely good swimmers with an average speed of 2.6 m/s, how far will it have traveled after 2.0 minutes?
240 m

11. Example 2
Ms. K and Zeus embark on a walk. If they leave Ms. K’s house, travel a distance of 1.2 km and return to the house in 12 minutes and 13 seconds, A) what was their average velocity?
B) What their average speed? Give your answer
in m/s
V=0
Speed- 1.6 m/s
The difference between speed and velocity is not just that velocity has a direction!!

12. Example 3
Zeus and Ms. K embark on a southbound journey. First they walk south at 6.5 km/hr for 1.1 hours. Then they stop to take a nap for 18 minutes and then continue south at 5.5 km/hr for 1.2 hours. A) What was their average velocity? B) What was their displacement?
V= 5.3 km/h

13. Example 4- Honors
To qualify for the finals in a racing event a race car must achieve an average speed of 250 km/h on a track with a total length of 2000 m. If a particular car covers the first half of the track at an average speed of 230 km/hr, what minimum average speed must it have in the second half of the event to qualify?
V=270 km/hr

14. One-Dimensional Motion
Graphing Position as a function of time

15. Objectives Draw and interpret distance versus time graphs
Interpret what the slope indicates
Differentiate between average velocity and instantaneous velocity

16. Distance Versus Time Graph
What is slope? The symbol?
What does the slope here indicate?????
M=rise/run m= change in y/change of x
VELOCITY!! Change in distance (position)/change in time

17. Example Distance Time What is the slope? What is the velocity?
Slope is 0, velocity is 0

18. Example Distance Time What is the slope? What is the velocity?
Slope is -, velocity is -, should be moving to the left

19. Example Distance Time What is the slope? What is the velocity?
Slope is +, velocity is +, moving to the right

20. Example
Distance
Time
What does this indicate about the velocity of the object at each part?
Part a- velocity is +, Part b- velocity is 0, part c-velocity is negative, but is moving faster than at part a because the slope is steeper

21. Instantaneous Velocity
Instantaneous velocity-velocity at a specific point in time
Examples?
Average Velocity-velocity over a time duration
Example?
Vf and Vi (instant) v=deltax/deltat (average)
Tangent lines are where instantaneous velocities are found

22. Example Distance 4m 2m 5 10 15 20 time (seconds)
time (seconds)
What is the velocity between 0-5 seconds?
Instant or average?

23. Example Cont Distance 4m 2m 5 10 15 20 time (seconds)
time (seconds)
What is the velocity between 5-10 seconds?
Instant or average?
2/5= .4m/s

24. Example Cont Distance 4m 2m 5 10 15 20 time (seconds)
time (seconds)
What is the velocity at 6 seconds? 9.8 seconds?
Instant or average? What is the velocity for 0-20 seconds?
What is the slope of the line? 2/5= .4 m/s for both
2/20= .1 m/s,, in this case instant velocity and average velocity will never be the same. Acceleration needs to be constant to have a point in which they are equal

25. One-Dimensional Motion
Acceleration

26. Objectives Define acceleration Solve acceleration problems
Draw and interpret velocity versus time and acceleration versus time graphs

27. Acceleration
The rate that velocity changes, so the change in velocity over the change in time
a= Δv/Δt = V f – V i / t f – t I
Units- m/s2
Vector or scalar?

28. Example
A sprinter goes from 10 m/s to 15 m/s in 5 seconds, at what rate is the sprinter accelerating?
15-10/5= 1 m/s^2

29. Example
I am driving east at 9.0 m/s and I see a deer and stop in 5.0 seconds
A=-1.8 m/s2 east, negative sign indicates that I am slowing down

30. Instantaneous Versus Average
Average acceleration-change in velocity over an interval of time
Instantaneous Acceleration-change in velocity at an instant of time

31. Example
A runner starts at a velocity of -1.2 m/s and speeds up constantly during a workout. After 25 minutes the treadmill has a velocity of -6.5 m/s. What is the average acceleration during this time?
A= m/s2 (3.5 x 10 -3)

32. Velocity Versus Time Graph
Slope=rise over run
What does slope indicate here?
What about other types of graphs?
Acceleration, Acceleration is positive

33. Example Velocity Time What does this tell us about the acceleration?
Acceleration is negative and constant

34. Example Continued Accel time
Acceleration is __________ and is below the time axis because _________________
Constant, the acceleration is negative

35. Example Continued What does the distance versus time graph look like?
A curve starting at the origin that rises steeply at first and then becomes a straight line

36. Example
Velocity
Time
Draw the acceleration vs time graph and the position vs time
Slope changes from positive to negative, direction does not change (remember slope here represent the acceleration). Acceleration graph- should be a straight line above the graph, and a straight line below in the middle
Position- should be an s, curve up before the middle, then the curve tapers off

37. One-Dimensional Motion
Uniformly Accelerated Motion

38. Objectives
Solve problems using uniform acceleration equations

39. Uniformly Accelerated Motion
Acceleration is constant
What would a velocity versus time graph look like with constant acceleration? Without constant?
Equations
V f = V i + at
Δx = V i Δt + ½ (a t2)
Vf2 = Vi2 + 2 a Δx
Δx = ½ (Vf – Vi) Δt
What variables do we have?
5 variables (vf, vi, Δx, Δt, a)
4 equations
If you know 3 variables you can find the other 2
1 happy physic student

40. Example
How long must a runway be for a plane to reach a takeoff velocity of 75 m/s if it accelerates at 20 m/s2?
Vi= 0
You can use Vf2 = Vi2 + 2 a Δx
Solve for Δx, Δx= 1400 m

41. Example
My tea tumbler falls off my car and slides along 95 South for 75 m. Friction slows my tumbler at 6 m/s2.
A)How fast was the car moving when the tumbler fell?
B)How long did it take the tumbler to stop?
Vi=30 m/s
T= 5 s

42. One-Dimensional Motion
Freefall

43. Objectives
Define freefall
Solve freefall problems

44. Freefall
If the only force acting upon an object is gravity the object is said to be in freefall
No _________________
Considered to be uniform accelerated motion
g is the acceleration due to gravity= 9.8 m/s2
When an object is in freefall we will use -9/8 m/s2
Does mass matter?
What would a distance versus time graph look like for a ball being thrown in the air?

45. Example
A ball is dropped from a height of 2.0 m. What is the velocity before it strikes the ground? How long did it take to hit the ground?
Motion is in the y direction, Δy is negative, when you solve for Vf answer will be positive. The calculator only gives the positive answer! Final velocity should be negative! Vf= -6.3 m/s, time=.64 seconds. You should never get a negative time!

46. Example Cont Draw the position, velocity, and acceleration graphs
Acceleration- constant since it is gravity, horizontal line at -9.8
Velocity-slope is -9.8, so there is a straight line starting at the origin and is below the time axis
Distance- line starts at 2, and curves down ward

47. Example continued
How long would it take for the same ball to be thrown up 2m and then fall to the ground?
T=.64 x 2= 1.28 m/s (1.3)
Since acceleration is constant, and the ending and beginning heights are the same, so the graphs are a mirror image. The time is just doubled.

48. Example
A ball is thrown straight down with a speed of 0.50 m/s from a height of 4.0 m. What is the speed of the ball 0.70 seconds after the ball is released?
Vi is negative since the ball is thrown down. Vf= -7.4 m/s (ball is still going down)

49. Example
A 0.25 kg baseball is thrown upward w/ a speed of 30 m/s. Neglect friction. What is the maximum height that the baseball reaches?
The final velocity here is 0, that is when the ball reaches the max height. Your initial velocity is + since the ball is traveling upward. Delta y=45.9 m