Which of the following
distance–time graphs shows an object initially moving with constant speed that stops
moving and then starts moving again with a lesser constant speed. Is it graph (A) or graph (B)?
Let’s look closely at the two
graphs at the same time and see what they describe.
We can see that each graph shows a
line. For each graph, the line starts at
the origin. And for each graph, the line
changes direction twice. We can define some points: point
zero, point one, point two, and point three. We can refer to these points when
describing the ways that the lines on the graphs change. Point zero is the origin of the
graph. Point one is where the line first
changes direction. Point two is where the line next
changes direction. And point three is the end of the
Both graphs show a straight line
from point zero to point one. And this tells us that both graphs
represent an object moving at a constant speed in a time interval. In both graphs, the line from point
one to point two is horizontal; that is, the distance does not change. So we know that the objects
represented by both graphs have stopped moving.
So far, the answer could be either
graph, so it comes down to the final part of the movement. The question asks, which object has
a speed when it starts to move again that is less than the initial speed of the
object? We know speed is represented by the
slope of a distance–time graph. So we’re looking for which graph
has a lesser slope between point two and point three than between point zero and
point one. We can see that the slope for graph
(B) is less for between point two and point three than it is between point zero and
point one. And so we know the correct answer
is option (B).