Chapter 2

- Motion in One Dimension

Kinematics

- In kinematics, you are interested in the

description of motion - Not concerned with the cause of the motion

Quantities for Motion

- Motion involves three concepts
- Displacement, Distance
- Velocity, Speed
- Acceleration

Position

- Defined in terms of a frame of reference
- One dimensional, so generally the x- or y-axis
- Defines a starting point for the motion

Displacement

- Defined as the change in position
- May be represented as ?y if vertical

Distance

- Distance relates to the actual path traveled.
- Displacement only depends on a different from

start to end. - Think of displacement as a net quantity.

Graph of Position with Time

Vector and Scalar Quantities

- Vector quantities need both magnitude (size) and

direction to completely describe them - Generally denoted by boldfaced type or an arrow

over the letter - or sign is sufficient
- Scalar quantities are completely described by

magnitude only

Speed

- The average speed of an object is defined as the

total distance traveled divided by the total time

elapsed - Speed is a scalar quantity (units m/s)

Velocity

- It takes time for an object to undergo a

displacement - The average velocity is the rate at which the

displacement occurs - Direction will be the same as the direction of

the displacement

Speed vs. Velocity

- Cars on both paths have the same average velocity

since they had the same displacement in the same

time interval - The car on the blue path will have a greater

average speed since the distance it traveled is

larger

Constant Velocity

- The straight line indicates constant velocity
- The slope of the line is the value of the average

velocity

Complex velocity

- The red line is for a time changing velocity
- The average velocity is the slope of the blue

line joining two points

Instantaneous Velocity

- The limit of the average velocity as the time

interval becomes infinitesimally short (I.e., as

the time interval approaches zero) - The instantaneous velocity is what happens at

each point of time - Its value is a tangent line at a point

Acceleration

- Changing velocity means an acceleration is

present - Acceleration is the rate of change of the

velocity - Units are m/s2 (SI), cm/s2 (cgs), and
- ft/s2 (US Cust)

Average Acceleration

Acceleration Quiz

- A car is traveling east and slowing down. Which

direction is its acceleration? - Is the acceleration considered to be positive or

negative? - What is the speed of an object like (stopped,

increasing, decreasing, or coasting) for a

constant but nonzero acceleration?

Another Quiz

- Match v(t) to a(t)

Relationship Between Acceleration and Velocity

Kinematic Equations

- For uniform acceleration

Graphical Interpretation

The Daytona 500

- What is the velocity of the race car after it has

traveled 100 feet if a5.00 m/s2 ?

Acceleration due to Gravity Free Fall

- Symbolized by g
- g 9.80 m/s2
- When estimating, use g 10 m/s2
- g is always directed downward
- toward the center of the earth
- Ignoring air resistance and assuming g doesnt

vary with altitude over short vertical distances,

free fall is constantly accelerated motion

Free Fall Problems