http://www.ck12.org Chapter 2. One-Dimensional Motion
Determining Average Velocity
If the motion is always in the same direction, the average velocity will have the same numerical value as the average
speed, except that a direction of motion must also be given.
If motion changes direction, though, the average velocity will be different than the average speed. Average velocity
depends on the total displacement, defined as the line from the final position from the initial position. If we assign
the zero position on the New Jersey side of the bridge, then when traveling to New York, the displacement is:
Pf−Pi=L−0. Traveling back from New York, the displacement isPf−Pi= 0 −L. The total displacement is
L+(−L) =0. The average velocity for the round trip over the bridge is 0 mph.
Check Your Understanding
A car moves due east at 30 mph for 45 min, turns around, and moves due west at 40 mph for 60 minutes. What is
the average velocity for the entire trip?
Answers:
East displacement: 30×^34 = + 22 .5 miles
West displacement:− 40 ( 1 ) =−40 miles
Total displacement:− 40 +(+ 22. 5 ) =− 17 .5 miles
Average velocity =− 117. 75.^5 =− 10 .0 mph
Instantaneous Velocity
As we said earlier, instantaneous speed is like the reading of a car’s speedometer. It is the speed at any exact point
in time. Instantaneous velocityrefers to velocity at a specific time, such ast= 3 .0 s. It is like the reading of a
speedometer combined with a pointer for current direction.
In practice, we cannot find a truly instantaneous velocity. Instead, we find an average velocity over smaller and
smaller intervals of time. For example, a modern car speedometer works by measuring the fraction of a second
it takes for the car’s wheels to turn once. For driving, this is close to instantaneous. When we measure average
velocity over a smaller and smaller intervals of time (∆t), we get closer and closer to instantaneous velocity.
The diagram below shows the position of an object at the timest 2 , 5.00 s andt 1 , 3.00 s. Ift 1 is held fixed andt 2
permitted to approacht 1 , the slope of the line betweent 2 andt 1 progressively comes closer to the slope of a tangent
line throught 1. The slope of the line throught 1 is called the instantaneous velocity att 1. In general, the slope of the
tangent line to a curve in a position-time graph gives the instantaneous velocity.