Video Transcript
What is average eastward velocity of an object that moves six meters east and two meters west in a total time of 0.75 seconds? Answer to one decimal place.
In this question, we’re being asked to find the average eastward velocity of an object. Let’s begin by using the information from the question to draw a sketch of the object’s motion. We’re told that the object moves six meters east and two meters west. So, if our object starts at this position here and we label our compass directions like this, then we can draw our object moving six meters to the east and two meters to the west, ending up at this position here. Since the question is asking us for a velocity, we should recall that the velocity of an object is defined as the displacement of that object divided by the time taken for that displacement to occur.
We can further recall that displacement is the straight-line distance between two positions. So the displacement of our object is the straight-line distance between its start position and its end position. This is represented by this blue arrow that we’ve labeled 𝑑. Now, displacement and velocity are both vector quantities, which means they have a direction as well as a magnitude. The magnitude of the object’s displacement is given by the length of the blue arrow. From our diagram, we can see that this length is equal to six meters minus two meters. And since the object ends up to the east relative to where it starts, then the direction of the displacement is to the east. Subtracting two meters from six meters gives a result of four meters. So we have that the displacement of the object is four meters to the east.
The question tells us that the time it takes for the object to move six meters east and two meters west is 0.75 seconds. Labeling this time 𝑡, we have that 𝑡 is equal to 0.75 seconds. So, we know the displacement of the object, and we know the time taken for this displacement to occur. Then, if we substitute these values into this equation, we can calculate the average velocity of the object. When we do this, we have that the velocity is equal to the displacement of four meters divided by the time of 0.75 seconds. And since the direction of the object’s displacement was to the east, then the direction of the average velocity is also to the east. When we evaluate this, we find that the average velocity of the object is 5.3 recurring meters per second to the east.
But we should notice that the question wasn’t actually asking us for the average velocity, but rather for the average eastward velocity. This means that we don’t actually need to include this bit that says that the velocity is to the east since the direction is already implicitly included in the term eastward velocity. So, we would say that the eastward velocity of the object is given by 5.3 recurring meters per second. Finally, we should notice that we are told to answer to one decimal place. Then our value of 5.3 recurring meters per second rounds to give us our final answer that, to one decimal place, the average eastward velocity of the object is equal to 5.3 meters per second.
