Video Transcript
The change in velocity of an object
over a four-second time interval is shown in the graph. What is the acceleration of the
object?
We are presented with a
velocity–time graph for an object, and we would like to find the acceleration of the
object. Let’s begin by labeling the graph
with the following points. The initial velocity 𝑢 has a value
of zero meters per second on the graph. Meanwhile, the final velocity 𝑣
has a value of six meters per second. The initial time 𝑡 sub zero has a
value of zero seconds, and the final time 𝑡 sub one has a value of four
seconds.
Now, let’s recall that the
acceleration 𝑎 of an object is related to the change in velocity of the object Δ𝑣
and the time interval in which the velocity changes Δ𝑡 by the formula 𝑎 equals Δ𝑣
divided by Δ𝑡. Since the acceleration is the rate
of change of velocity, the gradient of a velocity–time graph equals the acceleration
of an object. The change in velocity of the
object Δ𝑣 is given by the difference between the final velocity 𝑣 and the initial
velocity 𝑢. Substituting the values of the
final and initial velocities into this formula, we find that Δ𝑣 is equal to six
meters per second minus zero meters per second, which is just equal to six meters
per second.
The time interval in which the
velocity changes, Δ𝑡, is given by the difference between the final time 𝑡 sub one
and the initial time 𝑡 sub zero. Substituting the values of the
final and initial times into this formula, we find that Δ𝑡 is equal to four seconds
minus zero seconds, which is equal to four seconds.
We now have values for Δ𝑣 and Δ𝑡,
which we can substitute into the equation for acceleration. When we substitute in these values,
we find that the acceleration 𝑎 is equal to six meters per second divided by four
seconds. This gives us a value of 1.5 meters
per second squared for the acceleration of the object. And so, we have calculated the
acceleration of the object from the velocity–time graph. The acceleration is equal to 1.5
meters per second squared.
