a person walks first a constant speed of 5.00m/s along a straight line from point A to point B and then back along the line from point B to A at a constant speed of 3.00m/s. (a) what is her average speed over the entire trip? (b) what is her average velocity over the entire trip?
To find the average speed, you need to calculate the total distance traveled divided by the total time taken. Let's break down the problem step by step:
(a) To find the average speed:
- First, let's calculate the distance from point A to point B. Since the person is walking at a constant speed of 5.00 m/s, you need to determine the time taken to travel from A to B. Let's assume the distance is D, and the time taken is T1.
- Using the formula Distance = Speed × Time, we can rewrite it as D = 5.00 m/s × T1
- Now, let's calculate the distance from point B to point A. Since the person is walking at a constant speed of 3.00 m/s, you need to determine the time taken to travel from B to A. Let's assume the time taken is T2.
- Using the same formula Distance = Speed × Time, we can write it as D = 3.00 m/s × T2
- The total distance traveled for the entire trip will be twice the distance from A to B: 2D.
- The total time taken for the entire trip will be the sum of T1 and T2: T1 + T2.
- Now, we can find the average speed by dividing the total distance by the total time: Average Speed = (2D) / (T1 + T2).
(b) To find the average velocity:
- Velocity is a vector quantity that includes both magnitude (speed) and direction.
- In this case, the person walks from point A to point B and then back to point A, ending up at the same location.
- Since the person ends up at the same location, the displacement is zero, and the average velocity will also be zero.
Let's summarize the results:
(a) The average speed over the entire trip is (2D) / (T1 + T2).
(b) The average velocity over the entire trip is zero.
To find the specific values for average speed and velocity, you will need to know the actual distances traveled and times taken for each segment of the trip (from A to B and from B to A).
Average speed= vi+vf/2
Average speed= (5m/s +3m/s)/2
Average speed= 4 m/s