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 2.80 m/s.
(a) What is her average speed over the entire trip?
(b) What is her average velocity over the entire trip?
I thought that I could just take the average of the two speeds in part A but it isn't the answer. I don't know how to solve for it with no distance given for either A or B.
The average speed does not give the real average. You would need to take the harmonic mean of the speed, i.e.
mean speed = 1/(1/4.7 + 1/2.8)/2= 3.5 m/s
You can also find the average speed by assuming a distance of one (metre).
Total distance = 2
Total time = 1/4.7 + 1/2.8 = 0.57 sec.
Average speed = total distance / total time
= 2/0.57 = 3.5 m/s.
C.) What is her average velocity over the entire trip?
I was wondering how it is that we find out the velocity? I know that velocity would be change in X/change in time, but for the way the problem was set up, I'm not sure how to go about solving it.
If he makes a round trip, the distance is 2*D, where D is the distance for the single trip.
At the end of the round trip, his displacement is zero, because he ends up in the same place as before, irrespective of the history of what he did in the mean time.
Velocity = change in displacement / change in time = ?
To solve this problem, we can use the concept of average speed and average velocity. Average speed is defined as the total distance traveled divided by the total time taken, while average velocity is defined as the displacement divided by the total time taken.
(a) To find the average speed, we need to determine the total distance traveled and the total time taken for the entire trip. Since the person walks from point A to point B and then back to point A, the total distance traveled is twice the distance between A and B.
However, the problem does not provide the distance between points A and B. In this case, we can use the fact that speed is defined as the distance traveled divided by the time taken. Given the constant speed, we can set up an equation:
Speed = Distance / Time
For the first part of the trip from A to B, the speed is given as 4.70 m/s. Let's call the distance from A to B as d1. The time taken to travel this distance at a constant speed of 4.70 m/s is given by:
Time1 = d1 / 4.70 m/s
For the second part of the trip from B to A, the speed is given as 2.80 m/s. Let's call the distance from B to A as d2. The time taken to travel this distance at a constant speed of 2.80 m/s is given by:
Time2 = d2 / 2.80 m/s
Since the person traveled the same distance in each direction, d1 = d2.
To find the average speed, we need to know the total time taken for the entire trip, which can be calculated by adding the times taken for the two parts:
Total Time = Time1 + Time2
Once we have the total time, we can calculate the average speed using the formula:
Average Speed = Total Distance / Total Time
(b) To find the average velocity, we need to determine the displacement of the person and the total time taken for the entire trip. Displacement is a vector quantity that represents the change in position. Since the person walks from point A to B and back to A, the total displacement is zero because the starting and ending points are the same.
Therefore, the average velocity for the entire trip is zero.
In summary, to solve for the average speed, we need to know the distances from A to B and from B to A. Without this information, it is not possible to determine the average speed. However, we can still conclude that the average velocity is zero since the starting and ending points are the same.