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, V av : 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: