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Question Video: Predicting the Motion of an Object with Uniform Acceleration Science

The image shows the positions of an object at times one second apart. The object has uniform acceleration. Which color correctly shows the fourth position of the object?

04:35

Video Transcript

The image shows the positions of an object at times one second apart. The object has uniform acceleration. Which color correctly shows the fourth position of the object?

This question is asking us about the motion of an object that has uniform acceleration. To begin, let’s make sure we understand what this diagram is showing us. This diagram represents the motion of one object, an orange square, by showing it at different times one second apart. At first, the orange square is here. We’ll call this position one. Then, one second later, the orange square reaches this position. We’ll call this position two. Then, one second after that, the orange square is here. We’ll call this position three. The question is asking us where the orange square will be one second after this. These three different-colored squares represent different positions this may be.

For now, let’s just look at the first three positions of the orange object. Remember that we were told it has uniform acceleration. This means that the speed of the object increases by the same amount each second. Because the speed of the object is increasing, the distance traveled by the object in each second increases. Each second, the object will travel a greater distance than it did in the previous second. This is why the distance between position two and position three is greater than the distance between position one and position two.

Also, because the object is accelerating uniformly, the speed of the object increases at a uniform rate. This means that with every passing second, the distance that the object travels in a single second increases by the same amount. Every second, the object travels a farther distance than it did in the previous second. The important thing to remember is that the difference between each successive distance traveled is the same each time.

To help us understand this, let’s apply this idea to the orange object. The object starts out here, at position one. After one second, the object reaches position two. Notice that the distance traveled by the object in this time is equal to the width of the object. We’ll call this distance one unit. One second later, the object reaches position three. Because the object is accelerating, the distance between position two and position three is greater than the distance between position one and position two. In fact, this distance is equal to three times the width of the object, or three units.

So, in the first second, the object traveled a distance of one unit. But in the next second, the object traveled a distance of three units. Thus, the distance traveled by the object in a single second has increased by two units. Because the acceleration of the object is uniform, the distance it travels each second will keep increasing by two units each time. We can use this information to work out the location of position four.

The distance between position three and position four must be two units greater than the distance between position two and position three. This means that the distance between position three and position four must be equal to five units. So the fourth position of the object should be here.

Looking at the options given to us in the question, we see that this corresponds to the position shown in green. So this correctly shows the fourth position of the object.

To confirm our answer, we can double-check the other options. If we look at this position here, we can see that it’s the same distance from position three as position three is from position two. This suggests that the object would have moved the same distance as it did the previous second. This could only happen if the object had a constant speed during those two seconds. But we know the object is accelerating, so this cannot be correct.

Now, looking at the blue position, we can see that it’s much, much farther away than we would expect. This could only happen if the acceleration of the object had increased. But we know that the acceleration is uniform, so this cannot be the correct option either. Thus, we can be sure that the color that correctly shows the fourth position of the object is green.

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