Kinematics: The description of motion

Kinematics: The description of motion Dynamics: How the motion of objects changes under the influence of outside forces

Position We’re going to be studying motion “Motion” is a change in position “Position” is measured with respect to some reference frame, coordinate system, or axis

distance = total length of travel If you go from your house to the grocery store, then to your friend’s house, what total distance have you traveled?

displacement = change in position (how far from the starting point) Dx = xf - xi If you go from your house to the grocery store, then to your friend’s house, what is your displacement?

Which is true? A) Distance is always positive; Displacement is always negative B) Distance is always positive; Displacement can be positive or negative C) Displacement is always positive; Distance is always negative D) Displacement is always positive; Distance can be positive or negative E) Both distance and displacement can be positive or negative

Average speed and velocity How quickly position changes is going to be of interest There are several ways of specifying that…

Average speed and velocity How quickly position changes is going to be of interest There are several ways of specifying that…

Average speed and velocity How quickly position changes is going to be of interest There are several ways of specifying that… Example 1: A dog trots back to its owner with an average speed of 1.40 m/s from a distance of 2.3 m. How much time does it take for the dog to reach its owner?

Average speed and velocity How quickly position changes is going to be of interest There are several ways of specifying that…

Average speed and velocity How quickly position changes is going to be of interest There are several ways of specifying that… Example 2: An athlete sprints in a straight line for 50.0 m in 8.00 s, and then walks slowly back to the starting line in 40.0 s. If the “spring direction is taken to be positive, what are the… a) …average sprint velocity? b) …average walking velocity? c) …average velocity for the round trip?

As an object moves, its position changes. But at every instant of time, its position has some definite value. Therefore, its position is a function of time: x(t)…

Functions can be graphed…

Over this interval the average velocity is positive Average velocity can be seen on this graph as the slope of the line connecting two points Over this interval the average velocity is positive

Over this interval the average velocity is negative Average velocity can be seen on this graph as the slope of the line connecting two points Over this interval the average velocity is negative

Notice that the motion between the initial and final times is totally ignored. If you want to know what is happening at each moment, you need to introduce a new quantity…

Instantaneous velocity The slope of the tangent line at a given time This value changes at every moment

This figure shows the position-versus-time graph for an object This figure shows the position-versus-time graph for an object. Rank the instantaneous velocity of the object at points A, B, C, and D in order of increasing velocity, from smallest (most negative) to largest (most positive). A) A, B, C, D B) A, D, B, C C) C, B, D, A D) B, D, C, A E) D, B, C, A

One more not mentioned in the book: Instantaneous Speed This is simply the magnitude of the Instantaneous Velocity

Which does the speedometer in your car show? A) Average Speed B) Average Velocity C) Instantaneous Speed D) Instantaneous Velocity