1.3 Velocity and Speed

Key concepts: 

• Velocity = displacement / time

• Speed = distance / time

• Position, displacement, and velocity are some of the variables of motion.

• Equations of motion tie together variables of motion and allow us to model the motion using math.

Textbook sections:  2.3

Recall that velocity = displacement / time.  In math:

elocity and speed have dimensions of [distance] / [time], so their units will always be some kind of distance unit over some kind of time unit.  The SI unit is meters per second.

Remember the difference between displacement and distance?

• Displacement = [final position] - [initial position]

  • The sign matters!  A positive displacement means the object moved in the positive direction.  A negative displacement means that the object moved in the opposite direction.  (Remember that we picked the positive direction when we set up the frame of reference.)

  • Path does not matter!  Think of football.  A gain of 4 yards means that the ball ended up 4 yards down the field from its starting position.  We don't care what path the ball took as it was getting there.

• Distance = how far did the object go.

  • Path does matter now!  Again, football:  Suppose the ball goes 10 yards back from the line of scrimmage in the snap, and then it is run 15 yards forward.   That is a distance of 25 yards, but a displacement of 5 yards.

  • Sign does not matter.  Distance is always positive.

The difference between average and instantaneous velocity is in the size of the time interval in the denominator of the fraction.

• If the time interval is very small, we call the velocity "instantaneous."

• If the time interval is long, we call the velocity "average."

"Short" and "long" depend on the context.  If a particular motion takes many years, one day, or even one week is "short."  If the motion happens in 1/1000 second, then "long" might be 1 / 10,000 second!

Variables and Equations of Motion:  So far, we have used three variables to describe motion:  position, time, and velocity.  We have also begun to use equations of motion to tie those variables together.  For example, when I defined displacement

that was an equation of motion.  My definition of velocity is also an equation of motion.

Equations of motion are the spot where math meets physics. For a lot of students, this is the hard part. We’re used to using equations to calculate things, to get numerical answers. We will be doing that, of course, but we will also be using equations as a form of language to describe and understand things. In this case, the thing that we’re describing is motion, but the general idea — using equations as a language — is a pretty universal part of physics.

If we can describe a phenomenon with an equation, we can express the same information as the graph of that equation. Looking at the equation above, you might recognize something that looks like a slope equation.

If you can see it in the graph above, velocity is, in fact, the slope of a position vs. time graph. If you can’t quite see it yet, just take that on faith and we’ll explore it more in the practice problems and lab.

To Do:

• Try some problems: 5, 9, 11, 13

• Try this at home