# Question Video: Comparing the Distances Moved by Two Objects Plotted on the Same Distance-Time Graph Physics

The red and blue lines show the change in distance moved with time for two objects that have the same speed as each other. The distance moved by the object represented by the red line has a value of πβ and the distance moved by the object represented by the blue line has a value of πβ. The time between the start and end of the motion of the object represented by the red line is Ξπ‘β and the time between the start and end of the motion of the object represented by the blue line is Ξπ‘β. Which of the following is the relationship between πβ and πβ? [A] πβ > πβ [B] πβ < πβ [C] πβ = πβ

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### Video Transcript

The red and blue lines show the change in distance moved with time for two objects that have the same speed as each other. The distance moved by the object represented by the red line has a value of π one and the distance moved by the object represented by the blue line has a value of π two. The time between the start and end of the motion of the object represented by the red line is Ξπ‘ one and the time between the start and end of the motion of the object represented by the blue line is Ξπ‘ two. Which of the following is the relationship between π one and π two? Is it (a) π one is greater than π two, (b) π one is less than π two, or (c) π one is equal to π two?

If we take a look at our graph, we can see that we have distance on the vertical axis and time on the horizontal axis. For this part of the question, weβre interested in the distances π one and π two, where π one is the distance moved by the object represented by the red line and π two is the distance for the object represented by the blue line. The dashed lines on here show that the red and blue lines start at the same distance and also end at the same distance. The total distance moved by each object is equal to the change in value on the vertical axis only. So, the total distance moved by the two objects is the same, and therefore, π one is equal to π two.

Next, we need to find which of the following is the relationship between Ξπ‘ one and Ξπ‘ two. Is it (a) Ξπ‘ one is equal to Ξπ‘ two, (b) Ξπ‘ one is less than Ξπ‘ two, or (c) Ξπ‘ one is greater than Ξπ‘ two?

Now, remember that the question specifies that the values Ξπ‘ one and Ξπ‘ two refer to the time between the start and end of the motion of the objects. Therefore, Ξπ‘ one starts when the object represented by the red line starts moving, which is around here, and ends when the object stops moving, which is around here. So, itβs this interval of time here thatβs represented by Ξπ‘ one, whereas the object represented by the blue line starts moving sometime later. So, Ξπ‘ two starts around here and ends here. So, this interval here is Ξπ‘ two.

Now, there are no grid markings on this graph, so itβs difficult to tell by eye if those two intervals are the same. So, itβs helpful to recall that speed equals distance over time. Now, we found in the previous part of the question that π one is equal to π two. So, the two distances are the same. And in the question, weβre told that the two objects have the same speed. Therefore, the speed of the two objects is equal. And for two objects that have equal speeds and have covered equal distances, that means the time intervals must also be equal. Therefore, the relationship between Ξπ‘ one and Ξπ‘ two is (a) Ξπ‘ one is equal to Ξπ‘ two.