CK-12-Physics - Intermediate

http://www.ck12.org Chapter 2. One-Dimensional Motion

TABLE2.1: Mr. Jones’ Travels

Time Interval

(min)

Distance

(miles)

Speed

miles/min

Time Interval

(min)

Displacement

(miles)

Velocity

miles/min

[0, 2] 2.0 1.0 [0, 2] +2.0 +1

[2, 8] 0.0 0.0 [2, 8] 0.0 0

[8.10] 2.0 1.0 [8, 10] -2.0 -1

Look back at the position vs. time graph for Mr. Jones. Mr. Jones’ velocity during the time interval [0, 2] is
calculated using the definition of velocity:∆∆tx=(^2 ( 2.^0 −− 00 )). What is the slope of the line for the interval [0, 2]? A bit of
thought would lead you to the conclusion that the slope is identical to the definition of velocity, as long as the units
are included. In fact, the units of velocity are an aid in determining how to calculate velocity; miles “over” minutes
imply division. This is a very important result: any slope in a position vs. time graph has units of distance/time.
Therefore, the slope of the line in a position-time graph is velocity. During the interval [8, 10], the slope of the line is
negative. We can immediately surmise that the motion is toward the left on a conventional number line. During the
interval [2, 8], the line is horizontal, so the slope is zero, which in turn indicates that the velocity is also zero. This
conclusion makes sense physically, since Mr. Jones (and his car) are at the same position during the time interval [2,
8]. If his position is not changing, then of course, he’s not moving. So his velocity must be zero.

Let’s state some general conclusions regarding position-time graphs, using the sign conventions of a number line.

1. A positive slope indicates positive velocity; motion is to the right.


2. A negative slope indicates negative velocity; motion is to the left.


3. A horizontal line indicates zero velocity, the position remains unchanged.

Check Your Understanding

1. An ant travels with constant velocity from position +10 m to position -15 m for a time of 5 s; it instantaneously
   turns around, and moves from position -15 m to position +3 m with constant velocity, for a time of 6 s. Plot
   the ant’s motion in a position-time graph and indicate the ant’s velocity for each interval.

FIGURE 2.8

Answers: The ant has a velocity of -5 m/s over the first five seconds and a velocity of +3 m/s over the last six

seconds (Figure2.8).