A person walks first at a constant speed of 4.70 m/s along a straight line from point A to point B and then back along the line from B to A at a constant speed of 2.50 m/s.
To find the total distance traveled by the person, we need to calculate the distance covered in each leg of the journey separately and then add them together.
The distance covered in the first leg, from point A to point B, can be calculated using the formula:
Distance = Speed × Time
Given that the speed is 4.70 m/s, we need to find the time it takes to travel from A to B. To do this, we can divide the total distance between the two points by the speed:
Time = Distance / Speed
Let's assume the distance from A to B is D.
Therefore, the time taken to travel from A to B is:
Time_AB = D / 4.70
Now, let's calculate the distance covered in the second leg, which is the distance from B to A. Since the speed for this leg is 2.50 m/s, we can follow the same steps as above to find the time taken for this leg:
Time_BA = D / 2.50
Finally, to calculate the total distance traveled by the person, we add the distances covered in the two legs:
Total Distance = Distance_AB + Distance_BA
Now, let's substitute the values back into the equations to get the answer.
To solve this problem, we can use the formula for average speed:
Average speed = total distance / total time.
1. Find the distance from point A to point B:
The person walks at a constant speed of 4.70 m/s from point A to point B. Let's call the distance from A to B as distance AB.
We can use the formula for distance: distance = speed * time.
Let's assume the time taken to travel from A to B is t1. Therefore, distance AB = speed * t1.
Distance AB = 4.70 m/s * t1.
2. Find the distance from point B back to point A:
The person walks at a constant speed of 2.50 m/s from point B back to point A. Let's call the distance from B to A as distance BA.
We can use the formula for distance: distance = speed * time.
Let's assume the time taken to travel from B to A is t2. Therefore, distance BA = speed * t2.
Distance BA = 2.50 m/s * t2.
3. Find the total distance traveled:
The total distance traveled is the sum of distances AB and BA.
Total distance = distance AB + distance BA.
4. Find the total time taken:
The total time taken is the sum of times t1 and t2.
Total time = t1 + t2.
5. Calculate the average speed:
Using the formula average speed = total distance / total time, we plug in the values we have found:
Average speed = (distance AB + distance BA) / (t1 + t2).
This step-by-step breakdown should help you solve the problem and find the average speed of the person.
What is the question? Do you want the average speed? The average velocity?
The average speed is the distance traveled (in any direction)divided by the elapsed time. Let D be the distance between the points. 2D is the distance walked.
2D/V(average) = D/2.7 + D/4.5
D cancels out
Vaverage = 3.375 m/s