Distance-Time Graphs

Distance-Time Graphs
The Kentucky Derby is often described as the most exciting two minutes in sports. The
thoroughbred horses in this race run for a distance of 2 km. Their speeds change many
times during a race. How can we represent the motion of a racehorse? When you study
motion—the process of changing position—two measurements frequently compared are
distance and time. A graph that shows the comparison of distance over time is called a
distance-time graph.

Construct a Distance-Time Graph
To construct a distance-time graph, you need to measure and
record an object’s distance over time. Often scientists measure
the object’s distance from a starting point. That is because
objects sometimes change direction. 

Once distance and time measurements have been collected, a
distance-time graph is constructed. The time that the object is in
motion is plotted on the x-axis, and the distance is plotted on the
y-axis. The resulting distance-time graph provides a visual
representation of the object’s motion.

Interpret a Distance-Time Graph
Scientists use distance-time graphs to determine the motion of
an object. When an object moves the same distance each
second of travel, it moves at a constant speed. The resulting
distance-time graph is a straight line. 

You can also use distance-time graphs to compare the motion of
two different objects. Think about an object that is moving faster
than another object. The faster object will travel a greater
distance in the same amount of time. Steeper lines on distance-
time graphs indicate faster speeds.

The measurement of steepness is the slope. Recall that average speed s the total

distance traveled divided by the total time traveled. When you calculate the slope of a

distance-time graph, you divide the distance by the time. That means the slope of a

distance-time graph is the speed of the object.

Direction of Motion
Distance-time graphs show the distance an object is from its
starting point and also indicate the direction of the object's
motion. A positively sloped line indicates an object moves away
from the starting point. A negatively sloped line indicates an
object moves toward the starting point.

Objects at Rest
When an objects at rest, its distance remains the same. This type of motion is
represented by a horizontal line on a distance-time graph.

Distance-Time Graphs with Changing Speed
You learned that a distance-time graph is a straight line when an object moves at
constant speed. What happens if speed changes? The distance-time graph is curved. To
form a curve, the steepness of the line changes.

Slowing Down
When an object slows down, its speed decreases. That means that the slope of the
distance-time graph should get smaller over time. On a distance-time graph, slowing
down appears as a downward curve.

Speeding Up
When an object speeds up, its speed increases. That means that
the slope of the distance-time graph should get steeper over
time. On a distance-time graph, speeding up appears as an
upward curve.