1. Instructor: Dr. Tatiana Erukhimova
Physics 218: Mechanics
Instructor: Dr. Tatiana Erukhimova
Lecture 2

2. Motion in One Dimension (Chapter 2)
We consider a particle
- as time goes, the position of the particle changes

3. Velocity is the rate at which the position changes with time
Average velocity:

4. Consider motion of an object over a particular time interval
Consider motion of an object over a particular time interval. The displacement of the object is

5. Now consider an object moving to the left
Now consider an object moving to the left. The displacement of the object is

6. Average velocity: Average speed:
Velocity is the rate at which the position changes with time
Average velocity:
Average speed:

7. A person walks 70 m east, then 30 m west
A person walks 70 m east, then 30 m west. The total distance traveled is 100 m; the displacement is 40 m to the east.

8. The position of a runner as a function of time is plotted as moving along the x axis of a coordinate system. During a 3.00-s time interval, the runner’s position changes from x1 = 50.0 m to x2 = 30.5 m. What was the runner’s average velocity?
The runner’s average velocity is 6.50 m/s to the left.

9. You travel from CS to Houston
You travel from CS to Houston. First 20 miles to Navasota you cover in 20 min. You make a 10 min stop in Navasota and continue for another 20 min until you reach Hempstead which is 20 miles from Navasota. There you make a 15 min stop for lunch. Then you continue the remain 50 miles to Houston and reach it in 35 min. Find your average velocity.

10. Instantaneous Velocity

12. Instantaneous velocity equals the slope of the tangent to the curve at that point

14. Find the average velocity between 0s and 5s.
Find the instantaneous velocity at 2s, 5s

15. a) What was the velocity at t = 1.5s?
b) What was the velocity at t = 3s?

16. d) During what time interval was the car at rest?
e) What was the average velocity between t =0s and t = 5s?

17. Acceleration is the rate at which the velocity changes with time
Average acceleration

18. a) What was the acceleration at t = 2s?

19. b) What was the acceleration at t = 6s?

20. c) What was the acceleration at t = 7.5s?

21. d) During what time interval was the car moving at constant velocity?

22. e) How far did the car travel between t = 1s and t = 4s?

23. If a=ac=Const:

24. Problems
An experimental vehicle starts from rest at t=0 and accelerates at a rate given by a = 5 m/s3 t. What is its velocity and position 2 s later?
A particle moves along the x axis. Its position as a function of time is given by x(t) = at+bt2 where t is in sec and x is in meters. a and b are constants. What is the acceleration as a function of time?
a(t) = α t2. v(t = 0) = W; x(T) = D. α, T, W, and D are constants. Find the velocity and position as a function of time.

25. A “police car” problem x2 – x1 = 3.5 km x1 x2 x=0 V3=20m/s a=0
a=const
ap=kt
V(t=0)=0
You start moving from rest with constant acceleration. There is a police car hiding behind the tree. The policeman has a metric radar. He measures your velocity to be 30 m/s. While the policeman is converting m/s to mph, you continue accelerating. You meet another police car. This policeman measures your velocity to be 40 m/s. You also notice the police, drop your velocity to 20 m/s and start moving with a constant velocity. However, it is too late. This police car starts chasing you with acceleration kt (k is a constant). After some distance he catches you.

26. A “police car” problem x2 – x1 = 3.5 km x1 x2 x=0 V3=20m/s a=0
a=const
ap=kt
V(t=0)=0
1. What was your acceleration before you meet the second police car?
2. How long did you travel from x1 to x2?
3. Find x1
4. At which distance does the police car catch you?
5.Convert the velocity from m/s to mph

27. Free fall g=9.8 m/s2=32 ft/s2 g-positive!
On planet Earth, if you neglect air resistance, any body which is dropped will experience a constant acceleration, called g, independent of its size or weight.
g=9.8 m/s2=32 ft/s2
g-positive!

28. Galileo Galilei (1564-1624), the basic law of motion a = g = constv
Galileo Galilei ( ),
the basic law of motion
a = g = const
for all bodies independently on their masses

29. Galileo's “Law of Falling Bodies” distance (S) is proportional to time (T) squared

30. Galileo’s notes

31. Free fall

34. A ball is dropped vertically down (no air resistance) from height H.
Find the position x(t) and velocity v(t) of the ball as a function of time.
How long is the ball in the air?

35. A person throws a ball upward into the air with an initial velocity of 15 m/s. Calculate
How much time does it take for the ball to reach the maximum height?
How high does it go?
How long is the ball in the air before it comes back to the thrower’s hands
The velocity of the ball when it returns to the thrower’s hand
At what time t the ball passes a point 8.00 m above the person’s hand

36. A ball is thrown vertically upward with a velocity of magnitude v1 from a window at height H. What is the ball’s position and velocity at any time moment? How long does it take to reach the highest point? How long does it take to reach the ground? What is the velocity of the ball when it hits the ground?

37. A ball is thrown vertically upward with a velocity of magnitude v1 from a window at height H. In addition to gravity acting on the ball there is another force so that the acceleration in the up direction is –g+t where  is a constant and t is the time. What is the ball’s position when the acceleration is zero?

38. Have a great day! Chapter 3 video Reading: Chapters 2, 3
Chapters 2, 3 problems and exercises