The change in displacement of two objects with time is shown in the graph. The lines plotted on the graph are parallel. Do the two objects have the same velocity? Do the two objects have the same speed?
Taking a look at this graph, we see that it shows us object displacement versus time. The displacement versus time of two different objects, we’ll call this one the blue object and this one the red object, are represented on the graph. We know that these two lines are parallel. And we want to figure out if the blue object and the red object have the same velocity.
We can recall that an object’s velocity 𝑣 is equal to its displacement over some time interval 𝑡. Since our graph shows displacement versus time, that means the slope or the gradient of the curves on this graph represent the velocity of these objects. Therefore, if the slope of the blue line is the same as the slope of the red line, then regardless of their relative positions on the graph, they have the same velocity.
Normally, to figure out if these two lines have the same slope, we would need to calculate their numerical values. But in this case, we’re told that the two lines plotted on the graph are parallel to one another. This is another way of saying that they have the same exact slope. And since they have the same slope, that means they exhibit the same amount of displacement over the time interval 𝑡 that they’re moving.
In answer to our first question then, we can say that yes the two objects have the same velocity. Even though the velocity of the blue object is always positive or zero, while the velocity of the red object goes from positive to zero to negative, because of the definition of what velocity is, displacement divided by time, these two objects do have the same velocity.
Turning to our second question, we now want to know if the two objects have the same speed. Speed, it turns out, is related to velocity. In particular, the velocity of an object specifies the speed at which it moves and its direction of travel. For two objects to have the same velocity then, it means they must have the same speed and the same direction. Since we’ve already answered that our two objects have the same velocity, that means we can also say they have the same speed. And therefore, the red and the blue objects both have the same velocity and the same speed.