A person walks first at a constant speed of 5.10 m/s along a straight line from point circled A to point circled B and then back along the line from circled B to circled A at a constant speed of 3.15 m/s.(a) What is her average speed over the entire trip?
How can I find the average speed without knowing the distance?
To find the average speed without knowing the distance, you need to use the concept of time.
In this scenario, we have two parts to the trip: the outward journey from point A to point B, and the return journey from point B back to point A.
Let's denote the time taken for the outward journey as t1 and the time taken for the return journey as t2.
Given that the person walks at a constant speed of 5.10 m/s during the outward journey, we can determine the distance traveled during that time using the formula:
Distance = Speed × Time
So, the distance traveled from A to B is 5.10 m/s × t1.
Similarly, during the return journey, the person walks at a constant speed of 3.15 m/s. Therefore, the distance traveled from B to A is 3.15 m/s × t2.
Now, since average speed is defined as the total distance traveled divided by the total time taken, we can form an equation using the distances and times calculated above:
Average Speed = Total Distance / Total Time
The total distance is the sum of the distances traveled in both directions:
Total Distance = (5.10 m/s × t1) + (3.15 m/s × t2)
The total time is the sum of the time taken for the outward and return journeys:
Total Time = t1 + t2
Therefore, the equation becomes:
Average Speed = [(5.10 m/s × t1) + (3.15 m/s × t2)] / (t1 + t2)
Since we don't know the individual values of t1 and t2, we won't be able to calculate the average speed precisely without that information. However, if you are given specific values for t1 and t2, you can substitute them into the equation to calculate the average speed.