0.10 Phy1070: motion -- uniform and relative velocity  (Page 2/13)

Listings

• Listing 1 . A simple exercise on uniform velocity.
• Listing 2 . An exercise on average velocity.
• Listing 3 . Exercise #1 for a man on a train.
• Listing 4 . An exercise with three vectors in a plane.

Supplemental material

I recommend that you also study the other lessons in my extensive collection of online programming tutorials. You will find a consolidated index at www.DickBaldwin.com .

General background information

What is velocity?

Velocity is the time rate of change of position. Since displacement is the change of position, velocity is also the rate of displacement. Sincedisplacement is a vector quantity, velocity is also a vector quantity -- it has magnitude and direction.

An airplane may traverse 350 miles in a northeasterly direction in one hour. This statement describes a vector quantity (velocity) because it has bothmagnitude and direction.

The same airplane may traverse 350 miles in a southwesterly direction in one hour. This statement describes a different velocity. Even though the magnitudeis the same in both cases, the direction is different. Hence, the velocity is different.

What is speed?

Speed is distance covered in a unit of time without reference to direction. Since there is no reference to direction, speed is a scalar quantity.

A car may traverse 60 miles in one hour. An airplane may traverse 350 miles in one hour. An excellent runner may traverse one mile in three minutes. All ofthese statements describe scalar quantities (speed) since there is no reference to direction.

A person in a seat on a Ferris wheel may travel around the axle in the center of the wheel at a constant rotational speed. However, that person's velocity is notconstant. The velocity is continually changing because the direction of motion is continually changing.

Uniform velocity

Velocity is uniform when equal distances along a straight line are traversedin equal intervals of time. In this case

v = s/t

where

• v is uniform velocity
• s is the distance traveled (displacement)
• t is an interval of time

What about the direction?

Because uniform velocity occurs along a straight line, the computations involving uniform velocity, distance, and time may notnecessarily include the direction of that straight line. However, since both displacement and velocityare vector quantities, it is understood that the direction of velocity is the same as the direction of the displacement.

On the other hand, as you will see later, when combining two or more uniform velocities into a single resultant velocity, the directions of thedifferent uniform velocities becomes extremely important.

Speed, distance, and time

Note also that this same equation can be applied to computations involving speed, distance, and time where

• v represents speed and not velocity
• s is the distance traveled (not necessarily in a straight line)
• t is an interval of time

Units of velocity

The units of velocity are units of distance (such as meters) divided by units of time (such as seconds).

Discussion and sample code

Creation of tactile graphics

The module titled Manual Creation of Tactile Graphics explains how to create tactile graphics from svg files that I will provide.