Which of the lines shown on the
following distance–time graph represents the object with the greatest
acceleration? Is it (A) line A, (B) line B, (C)
line C, or (D) the objects have equal acceleration?
The question is asking us about the
accelerations of some objects. So let’s remind ourselves first of
the definition of acceleration. Acceleration is defined as the rate
of change of speed. In other words, the acceleration of
an object is given by how much the speed of an object changes divided by the time
taken for the change to occur. It is the change in speed divided
by the change in time.
On the distance–time graph, the
horizontal axis represents changes in time and the vertical axis represents changes
in distance. Looking at the three lines on the
graph, we can see that they are all straight.
Recall that on a distance–time
graph, the slope of a line corresponds to the speed of the object that the line
represents. And since each of these lines has a
constant slope, each line represents an object moving at a constant speed. Each line has a different slope and
therefore represents a different speed. Line A has a greater slope than
line B, and line B has a greater slope than line C. We therefore know that the speed of
A is greater than the speed of B, which is greater than the speed of C.
It is important to understand that
although the speeds shown are all different, none of the speeds are changing. They’re all constant values of
speed. Therefore, none of the objects are
accelerating. The acceleration for all the
objects is zero. This means that the correct answer
to the question is option (D). All of the objects have equal
acceleration, specifically zero.