Ch. 1: Kinematics in One Dimension

Object of interest Observer Object whose motion we are describing Observer Person who is doing the describing In order to describe the motion of something, we need to identify the observer.

Reference frame Object of reference Includes: Object of reference Coordinate system w/ scale for measuring distances Clock (origin in time t=0)

Linear motion or one-dimensional motion A model of motion that assumes that a (point-like) object moves along a straight line

Why do physicists say, “Motion is relative?” Relative motion depends on where the observer is. When you are driving, you are not moving with respect to the car, but you are moving relative to people on the sidewalk.

1.2 Motion Diagrams Velocity arrows indicate which way and how fast the object is moving. The longer the arrow, the faster the motion. Vector quantity Has a direction as well as magnitude Scalar quantity Only magnitude https://www.youtube.com/watch?v=A05n32Bl0aY

Velocity change arrows Indicates the velocity between two points increased or decreased.

Velocity change arrows Delta means "change in." Change always means final minus initial: what it is now compared to what it was before. The arrow above v reminds us that velocity is a vector; it has both magnitude and direction. © 2014 Pearson Education, Inc.

Finding velocity change arrows Consider two adjacent velocity vectors, in this example at points 2 and 3. Find which vector would need to be added to the velocity corresponding to point 2 to get the velocity corresponding to point 3. © 2014 Pearson Education, Inc.

1.3 Quantities for describing motion Time – clock reading Time interval – difference of two times (t2-t1) or Δt

Quantities for describing motion Position Location with respect to a particular coordinate system Displacement Vector that starts from object’s initial position and ends at final position Distance/Path length How far object moved as it traveled

Review question 1.3 Sammy went hiking between two camps that were separated by about 10 km. He hiked approximately 16 km to get from one camp to the other. Draw a diagram of this and translate 10 km and 16 km into the language of physical quantities.

1.4 Representing Motion Kinematics – description of motion Data Tables Position vs. Time graph Trendline

Review Question 1.4 Look at position vs. time graph in Figure 1.10. What are the positions of the object at clock readings 2.0 s and 5.0 s?

Constant Linear Motion

The slope of the position vs. time graph represents velocity The slope gives info about Speed Direction Velocity equation

Rearrange equation

Constant velocity

Displacement is the area between the line and the time axis.

1.6 Motion at constant acceleration

When velocity is not constant On a velocity-versus-time graph, velocity will be a straight line only if it is constant. Instantaneous velocity is the velocity of an object at a particular time. Average velocity is the ratio of the change in position and the time interval during which this change occurred. For motion at constant velocity, the instantaneous and average velocities are equal; for motion with changing velocity, they are not. © 2014 Pearson Education, Inc.

Acceleration characterizes the rate at which the velocity of an object is changing The simplest type of linear motion with changing velocity occurs when the velocity of the object increases or decreases by the same amount during the same time interval (a constant rate of change). In this simple case, the velocity-versus-time graph will be linear. © 2014 Pearson Education, Inc.

Finding acceleration from a velocity-versus-time graph Acceleration is the slope of the velocity-versus-time graph: A larger slope indicates the velocity is increasing at a faster rate. Velocity is a vector quantity; therefore acceleration is also a vector quantity. The average acceleration of an object during a time interval is © 2014 Pearson Education, Inc.

Acceleration © 2014 Pearson Education, Inc.

When is acceleration negative? Acceleration can be positive or negative. If an object moving in the positive direction is slowing down, its velocity-versus-time graph has a negative slope, corresponding to a decreasing speed and negative acceleration. An object can have a negative acceleration and speed up! Consider an object moving in the negative direction with a negative component of velocity, but whose speed is increasing in magnitude. © 2014 Pearson Education, Inc.

Determining the velocity change from the acceleration From the slope of the velocity-versus-time graphs, we see ax = (vx − v0x)/(t−t0), or ax (t−t0) = (vx − v0x) Set t0 = 0 to simplify (the clock starts at 0) and move v0x to the other side: vx = v0x + axt © 2014 Pearson Education, Inc.

Displacement of an object moving at constant acceleration © 2014 Pearson Education, Inc.

Position as a function of time The equation for displacement can be found from the area between the velocity-versus-time graph line and the time axis. © 2014 Pearson Education, Inc.

Position of an object during linear motion with constant acceleration © 2014 Pearson Education, Inc.

Graph of position versus time for constant acceleration motion Position is quadratic in time (there is a t2 term), so the graph is parabolic. The slopes of the tangent lines (indicating the instantaneous velocity) are different for different times. © 2014 Pearson Education, Inc.

Example 1.7

Three equations of motion © 2014 Pearson Education, Inc.

1.8 Free fall

Free Fall is……. When an object falls towards the earth due to gravity. Velocity increases as object free falls.

Free fall The hypothetical motion of falling objects in the absence of air is a model of the real process and is called free fall. Galileo hypothesized, based on experiments, that free fall occurs exactly the same way for all objects regardless of their mass and shape. Galileo hypothesized that speed increases in the simplest way—linearly with time of flight; the acceleration of free-falling objects is constant. © 2014 Pearson Education, Inc.

Mathematics of free fall The acceleration of objects in free fall is given a special symbol g: We replace x with y in our equations of motion for constant acceleration because free fall is placed along the vertical axis. These equations use the choice that the positive y-axis is downward! © 2014 Pearson Education, Inc.

Motion diagrams and graphs for free fall © 2014 Pearson Education, Inc.

Acceleration due to gravity g is an acceleration!!!!!! Not a force g is constant!!!!!!! It does not change g = 9.8 m/s2 downward

Example Jordan is riding Scream at Fiesta Texas. If Jordan free-falls for 3.7s, what will be her change in distance after 3.7 seconds? What is her velocity at this time?

https://www.youtube.com/watch?v=8RKAb5accC0 MIT Physics – ball and feather in vacuum http://www.physicsclassroom.com/class/1dkin/u1l5b.cfm