The distance between position 𝐴 and position 𝐵 shown in the diagram is 2,500 meters. What is the average speed of a car that travels from 𝐴 to 𝐵 in 200 seconds?
Okay, so in this question, we have a car traveling between position 𝐴 and position 𝐵. We’re told that the distance between position 𝐴 and position 𝐵 is equal to 2,500 meters. If we recall that distance is defined as the length of a path between two positions, then we can see that this distance of 2,500 meters must be equal to the length of the path drawn in the diagram between position 𝐴 and position 𝐵. We’ll label this distance as 𝑑, and then we can say that 𝑑 is equal to 2,500 meters.
We have a car that is traveling along this path from 𝐴 to 𝐵. And we’re told that it takes a time of 200 seconds to do this. If we call this time 𝑡, then we can say that 𝑡 is equal to 200 seconds. So we know the distance that the car travels, and we know the time that it takes to travel this distance. The question is asking us to find the average speed of the car. We can recall that there is a formula which relates the three quantities speed, distance, and time. Specifically, the average speed of an object traveling between two positions is equal to the total distance traveled by that object divided by the total time taken to cover that distance.
If we label this average speed as 𝑠, then we can write this more concisely as 𝑠 is equal to 𝑑, the distance, divided by 𝑡, the time taken. We know the values of both the distance 𝑑 and the time 𝑡. So if we substitute those values into this formula, then we can calculate 𝑠, the average speed of the car. Doing this gives us that 𝑠 is equal to our distance of 2,500 meters divided by our time of 200 seconds. Then, evaluating this gives us a result of 12.5 meters per second. And so our final answer is that the average speed of the car is equal to 12.5 meters per second.