1. Motion in a Straight Line
Chapter 2
Motion in a Straight Line

2. Linear motion In this chapter we will consider moving objects:
Along a straight line
With every portion of an object moving in the same direction and at the same rate (particle-like motion)

3. Distance, position, and displacement
Distance a total length of the path traveled regardless of direction (SI unit: m)
In each instance we choose an origin – a reference point, convenient for further calculations
Position of an object is described by the shortest distance from the origin and direction relative to the origin
Displacement – a change from position x1 to position x2

4. Velocity and speed
Average speed - a ratio of distance traveled (over a time interval) to that time interval (SI unit: m/s)
Average velocity - a ratio of displacement (over a time interval) to that time interval
Instantaneous velocity – velocity at a given instant
Instantaneous speed – a magnitude of an instantaneous velocity

5. Velocity and speed

6. Velocity and speed

7. Instantaneous velocity
The instantaneous velocity is the slope of the line tangent to the x vs. t curve
This would be the green line
The light blue lines show that as Δt gets smaller, they approach the green line

8. Acceleration
Average acceleration - a ratio of change of velocity (over a time interval) to that time interval (SI unit = (m/s)/s = m/s2)
Instantaneous acceleration – a rate of change of velocity at a given instant

9. Acceleration The blue line is the average acceleration
The slope (green line) of the velocity-time graph is the acceleration

10. Chapter 2
Problem 43
You allow 40 min to drive 25 mi to the airport, but you’re caught in heavy traffic and average only 20 mi/h for the first 15 min. What must your average speed be on the rest of the trip if you’re to make your flight?

11. Case of constant acceleration
Average and instantaneous accelerations are the same
Conventionally
Then

12. Case of constant acceleration
Average and instantaneous accelerations are the same
Conventionally
Then

13. Case of constant acceleration

14. Case of constant acceleration

15. Case of constant acceleration To help you solve problems
Equations
Missing variables

16. Chapter 2
Problem 36
You’re driving at speed v0 when you spot a stationary moose on the road, a distance d ahead. Find an expression for the magnitude of the acceleration you need if you’re to stop before hitting the moose.

17. Case of free-fall acceleration
At sea level of Earth’s mid-latitudes all objects fall (in vacuum) with constant (downward) acceleration of
a = - g ≈ m/s2 ≈ - 32 ft/s2
Conventionally, free fall is along a vertical (upward) y-axis

18. Chapter 2
Problem 37
You drop a rock into a deep well and 4.4 s later hear a splash. How far down is the water? Neglect the travel time of sound.

19. Graphical representation

20. Graphical representation

21. Graphical representation

22. Graphical representation

23. Graphical representation

24. Graphical representation

25. Graphical representation

26. Graphical representation

27. Graphical representation

28. Questions?

29. Answers to the even-numbered problems
Chapter 2
Problem 14:
(a) 24 km
(b) 9.6 km/h
(c) - 16 km/h
(d) 0 km
(e) 0 km/h

30. Answers to the even-numbered problems
Chapter 2
Problem 24:
15 m/s2

31. Answers to the even-numbered problems
Chapter 2
Problem 26:
31 s

32. Answers to the even-numbered problems
Chapter 2
Problem 28:
100 m

33. Answers to the even-numbered problems
Chapter 2
Problem 38:
11 m/s

34. Answers to the even-numbered problems
Chapter 2
Problem 42:
3.8 m/s2