two hours elapse as it moves that distance. The car’s average velocity equals +50 miles
divided by two hours, or +25 mi/h (+40 km/h). Note that the direction is positive because
the displacement was positive. If the displacement were negative, then the velocity
would also be negative.
At this point in the discussion, we are intentionally ignoring any variations in the car’s
velocity. Perhaps the car moves at constant speed, or maybe it moves faster at certain
times and then slower at others. All we can conclude from the information above is that
the car’s average velocity is +25 mi/h.
Velocity has the dimensions of length divided by time; the units are meters per second
(m/s).
ǻx = displacement
ǻt = elapsed time
Units: meters/second (m/s)
What is the mouse’s velocity?
2.4 - Average velocity
Average velocity: Displacement divided by
elapsed time.
Average velocity equals displacement divided by the time it takes for the displacement
to occur.
For example, if it takes you two hours to move positive 100 miles (160 kilometers), your
average velocity is +50 mi/h (80 km/h). Perhaps you drive a car at a constant velocity.
Perhaps you drive really fast, slow down for rush-hour traffic, drive fast again, get pulled
over for a ticket, and then drive at a moderate speed. In either case, because your
displacement is 100 mi and the elapsed time is two hours, your average velocity is
+50 mi/h.
Since the average velocity of an object is calculated from its displacement, you need to
be able to state its initial and final positions. In Example 1 on the right, you are shown
the positions of three towns and asked to calculate the average velocity of a trip. You must calculate the displacement from the initial to final
position to determine the average velocity.
A classic physics problem tempts you to err in calculating average velocity. The problem runs like this: “A hiker walks one mile at two miles per
hour, and the next mile at four miles per hour. What is the hiker's average velocity?” If you average two and four and answer that the average
velocity is three mi/h, you will have erred. To answer the problem, you must first calculate the elapsed time. You cannot simply average the two
velocities. It takes the hiker 1/2 an hour to cover the first mile, but only 1/4 an hour to walk the second mile, for a total elapsed time of 3/4 of an
hour. The average velocity equals two miles divided by 3/4 of an hour, which is a little less than three miles per hour.
Average velocity
Displacement divided by elapsed time