The figure shows a velocity–time graph for a car moving in a straight line. Given that 𝑣 is measured in meters per second and 𝑡 in seconds, determine when the car is moving forward.
So here we have a velocity–time graph. Let’s begin by recalling what we know about velocity. Velocity is a vector quantity. It can be defined both by its magnitude and its direction. We say that the magnitude of velocity is speed. And so this means velocity can be both positive or negative. We need to define a positive direction. And once we’ve done that, we can say that when the velocity is positive, it’s moving in that direction. And when it’s negative, it’s moving in the opposite direction.
Now, the question is asking us to determine from the graph the times at which the car is moving forward, in other words, the time at which the velocity is positive. It needs to be greater than zero. Now we can read these portions straight from the graph. We see that their velocity is greater than zero here, it’s greater than zero here, and then it’s still greater than zero here. We need to be careful with this last portion. At this portion between 𝑡 equals 11 and 𝑡 equals 12, the velocity is zero. So the car is neither moving forward nor backward.
Similarly, in each section that lie below the 𝑡-axis, the velocity is always negative. For instance, here, the velocity is negative four, and so at this point the car must be moving backward. The first part of our graph shows that the car is moving forward from 𝑡 equals zero to 𝑡 equals two seconds. The second part that we’re interested in is values of 𝑡 from six to 11 seconds. And so we can say that from our velocity–time graph, we see that the car is moving forward from 𝑡 equals zero to two seconds and 𝑡 equals six to 11 seconds.