Summary and Main Ideas

Summary of lessons so far

The following are the main ideas from the past few lessons:

Displacement and Distance

• Kinematics is the study of motion without considering its causes. When it is limited to motion along a straight line, called one-dimensional motion.
• Displacement is the change in position of an object.
• In symbols, displacement \(\Delta x\) is defined to be
  \(\Delta x = x_{\text{f}} - x_0,\)
  where \(x_0\) is the initial position and \(x_{\text{f}}\) is the final position. In this tutorial, the Greek letter \(\Delta\) (delta) always means “change in” whatever quantity follows it. The SI unit for displacement is the meter (m). Displacement has a direction as well as a magnitude.
• When you start a problem, assign which direction will be positive.
• Distance is the magnitude of displacement between two positions.
• Distance traveled is the total length of the path traveled between two positions.

Vectors and Scalars

• A vector is any quantity that has magnitude and direction.
• A scalar is any quantity that has magnitude but no direction.
• Displacement and velocity are vectors, whereas distance and speed are scalars.
• In one-dimensional motion, direction is specified by a plus or minus sign to signify left or right, up or down, and the like.

Time, Velocity and Speed

• Time is measured in terms of change, and its SI unit is the second (s). Elapsed time for an event is
  \(\Delta t = t_{\text{f}} - t_0,\)
  where \(t_{\text{f}}\) is the final time and \(t_0\) is the initial time. The initial time is often taken to be zero, as if measured with a stopwatch; the elapsed time is then just \(t\).
• Average velocity \(\bar{v}\) is defined as displacement divided by the travel time. In symbols, average velocity is
  \(\bar{v} = \cfrac{\Delta x}{\Delta t} = \cfrac{x_\text{f} - x_0}{t_\text{f} - t_0}.\)
• The SI unit for velocity is m/s.
• Velocity is a vector and thus has a direction.
• Instantaneous velocity \(v\) is the velocity at a specific instant or the average velocity for an infinitesimal interval.
• Instantaneous speed is the magnitude of the instantaneous velocity.
• Also, instantaneous speed is a scalar quantity, as it has no direction specified.
• Average speed is the total distance traveled divided by the elapsed time. (Average speed is not the magnitude of the average velocity.) Speed is a scalar quantity; it has no direction associated with it.

Glossary of Words

Average speed

distance traveled divided by time during which motion occurs

Average velocity

displacement divided by time over which displacement occurs

Displacement

the change in position of an object

Distance

the magnitude of displacement between two positions

Distance traveled

the total length of the path traveled between two positions

Elapsed time

the difference between the ending time and beginning time

Instantaneous velocity

velocity at a specific instant, or the average velocity over an infinitesimal time interval

Instantaneous speed

magnitude of the instantaneous velocity

Kinematics

the study of motion without considering its causes

Model

simplified description that contains only those elements necessary to describe the physics of a physical situation

Position

the location of an object at a particular time

Scalar

a quantity that is described by magnitude, but not direction

Time

change, or the interval over which change occurs

Vector

a quantity that is described by both magnitude and direction