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

a time changing velocity line is for The average velocity is the slope of the points

blue

line joining two

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/s 2 ft/s 2 (US Cust) (SI), cm/s 2 (cgs), and

Average Acceleration

Acceleration Quiz 1.

2.

3.

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 a=5.00 m/s 2 ?

Acceleration due to Gravity: Free Fall     Symbolized by g g = 9.80 m/s 2  When estimating, use g  10 m/s 2 g is always directed downward  toward the center of the earth Ignoring air resistance and assuming g doesn’t vary with altitude over short vertical distances,

free fall is constantly accelerated motion

Free Fall Problems