Kinematics Kinematics is the branch of physics that describes the motion of points, bodies (objects) and systems of bodies (groups of objects) without consideration of the causes of motion.

Kinematics One-dimensional kinematics involves movement along one axis. We set up a one dimensional coordinate system with an x axis and the origin at x=0 Position – the position in our coordinate system is the value of x.

Figure 2-1 A One-Dimensional Coordinate System

Kinematics Distance – the total length of travel. It always has a positive value. It is a scalar quantity – completely characterized only by magnitude. SI unit: meter

Kinematics Displacement – the change in position Δx. It is a vector quantity completely characterized by magnitude and direction. Δx=x f -x i SI unit: meter, m Δx can be positive, negative or zero.

Kinematics Average speed – distance divided by elapsed time. Average velocity – displacement divided by elapsed time. SI unit for speed and velocity:

Kinematics Instantaneous speed – the magnitude of velocity at a given instant. Instantaneous velocity – the velocity at a given instant.

Kinematics Average acceleration – the change in velocity divided by the change in time.

Kinematics Instantaneous acceleration – the acceleration at a given instant.

Kinematics Constant acceleration – when acceleration is constant, instantaneous acceleration is equal to the average acceleration. In this course we will only be dealing with situations involving constant acceleration (with one exception).

Kinematics In the following slide quantities with the subscript 0 refers to the value of a quantity at the beginning of an event, and the quantities without a subscript refers to the value of a quantity at the end of an event. Δt becomes t if t 0 =0 Frequently the quantities with the subscript 0 equal zero, and drop out from the equations.

Table 2-4 Constant-Acceleration Equations of Motion Variables RelatedEquationNum ber Velocity, time, acceleration v = v 0 + at 2-7 Initial, final, and average velocity v average = ½(v 0 + v) 2-9 Position, time, velocity x = x 0 + ½(v 0 + v)t 2-10 Position, time, acceleration x = x 0 + v 0 t + ½ at Velocity, position, acceleration v 2 = v a(x – x 0 ) = v a  x 2-12

Free Fall Free fall refers to an object falling freely only under the influence of gravity.(Negligible air resistance)

Free Fall It could refer to a body falling toward another body, or to body orbiting another body.

Free Fall Near the surface of the Earth the acceleration of gravity, is on the average

Free Fall When dealing with objects in free fall, we substitute g for a. g has a positive value, but if we define up as the positive direction, the acceleration of a freely falling object becomes -g