A person walks first at a constant speed of 4.50 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 3.00 m/s.
There is no question here. If you submit it again, show your work.
A person walks first at a constant speed of 4.50 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 3.00 m/s.
(a) What is her average speed over the entire trip?
(b) What is her average velocity over the entire trip?
Since different lengths of time are spent walking in each direction, you can't just take the average of the two numbers. If v is the average speed,
1/v = (1/2) (1/4.5 + 1/3.0)
= (1/2)(2/9 + 3/9) = 5/18
v = 18/5 = 3.6 m/s
How can you derive that?
Let L be the distance between A and B
v*T = 2L defines tha average speed v
T = L/V1 + L/V2 = L(1/V1 + 1/V2)
1/v = T/2L = (1/2)(1/V1 + 1/V2)
The average velocity is the distance between start and finish points divided by elapsed time. Consider where you ended up and the answer will be obvious.
To find the total distance traveled and the total time taken, we can use the equation:
Distance = Speed × Time
1. First, let's find the distance traveled from point A to point B.
Given:
Speed from A to B = 4.50 m/s
To find the distance, we need to know the time taken. Let's assume it as "t" seconds.
Distance from A to B = Speed × Time
Distance from A to B = 4.50 m/s × t
2. Now, let's find the distance traveled from point B to point A.
Given:
Speed from B to A = 3.00 m/s
Again, we assume the time taken as "t" seconds.
Distance from B to A = Speed × Time
Distance from B to A = 3.00 m/s × t
3. The total distance traveled is the sum of the distances from A to B and from B to A.
Total Distance = Distance from A to B + Distance from B to A
Total Distance = (4.50 m/s × t) + (3.00 m/s × t)
4. The total time taken is the sum of the times spent from A to B and from B to A.
Total Time = Time from A to B + Time from B to A
Total Time = t + t = 2t
So, the total distance traveled is (4.50 m/s × t) + (3.00 m/s × t) and the total time taken is 2t.
Note: We're assuming that the time taken from A to B is the same as the time taken from B to A.
To get specific values for the total distance and the total time, we need to know the value of "t" or have additional information.