The figure shows a velocity–time graph of a particle moving in a straight line. When is the particle’s acceleration zero?
We’re given a graph that represents the velocity 𝑣 of a particle at time 𝑡. And we’re looking to find some information about the acceleration. So we’re going to begin by linking acceleration with velocity. We know that the definition of acceleration is rate of change of velocity. And so if we’re given an expression for 𝑣 in terms of time 𝑡, we can differentiate that with respect to time to find an expression for acceleration. We also know that the derivative represents the slope of a curve.
And so if we consider this graphically, we can say that acceleration is the slope of the velocity–time graph. And we can therefore reword our question and ask ourselves, well, when is the slope of our graph zero? The slope of the graph looks like a horizontal line. And we see that that occurs over here and over here.
Another way of saying this is that the velocity of the graph remains constant at these points. If we read off of the 𝑡-axis or the horizontal axis, we can see that the slope of our graph is zero from 𝑡 equals four to 𝑡 equals six and from 𝑡 equals 10 to 𝑡 equals 13. We’re not given any units for our time in this question. So we can say that these are in time units.
The acceleration of the particle is zero from 𝑡 equals four to 𝑡 equals six and 𝑡 equals 10 to 𝑡 equals 13.