physics 2011 chapter 2: straight line motion. motion: displacement along a coordinate axis (movement...

Physics 2011

Chapter 2:

Straight Line Motion

Motion:

• Displacement along a coordinate axis (movement from point A to B)

• Displacement occurs during some interval of Time

Describing Motion:

• Average Velocity, Vav: The speed of displacement as characterized by the ratio of a change in displacement to its corresponding change in time

Describing Motion (Cont.)

• Average Acceleration: The “Speed of Velocity” as characterized by measuring a change in velocity and its corresponding change in time

Problem with Average Quantities• Velocity is different at every point on the

curve

Instantaneous Velocity, V

• Need to have a more accurate description of velocity

• A description that is valid at a particular point during the time interval of interest

• If we can write a time based function describing displacement, x(t), then velocity is just the derivative of that function.

Instantaneous Acceleration• Likewise, a more accurate description of acceleration is

useful• Given an instantaneous velocity as a function of time, v(t),

the instantaneous acceleration is the first derivative of the velocity function with respect to time

• By definition then, Acceleration is also the Second Derivative of the displacement function, x(t), with respect to time.

General Equations, Integral Form:

• In general then, since velocity is the derivative of displacement and acceleration is the derivative of velocity:

• Given an acceleration as some function of time, a(t):

Constant Acceleration

• If we don’t allow Acceleration to be a time varying function (For simplicity and also because there are many examples of constant acceleration, such as gravity):

Kinematic Diagrams

• Given some kind of Motion, it is possible to draw curves and graphs of the motion based on the equations described in the chapter.

• Such graphs of motion are called Kinematic (derived from the word Kinetic, relating to motion) Diagrams

Motorcycle in Motion:

Motorcycle Motion Data:

Kinematic Diagram of Motorcycle Motion: