Wilma i. ball walks at a constant speed of 5.93 m/s along a straight line from point a to point b and then back from b to a at a constant speed of 3.15 m/s.
(a) what is wilma's average speed over the entire trip?
(b) what is wilma's average velocity over the entire trip?

a) The average speed is 4.11 m/s

b) The average velocity is zero.

Explanation:

Hi there!

a) The average speed is calculated as the traveled distance over the time taken to cover that distance:

a.s = d/t

Where:

a.s = average speed.

d = traveled distance.

t = time.

From A to B Wilma travels at a constant speed of 5.93 m/s. So, we can write the equation of average speed as follows:

5.93 m/s = d / t1

Where t1 is the time taken to travel the distance from A to B (d)

From B to A Wilma travels at 3.15 m/s, so the equation of average speed could be written as follows:

3.15 m/s = d / t2

Where t2 is the time taken to travel from B to A (d)

If we solve both equations for the time, we can get the total time of the trip by adding the expressions we obtain:

t1 = d / 5.93 m/s

t2 = d / 3.15 m/s

The total time of the trip is the sum of both times:

t1 + t2 = d / 5.93 m/s + d / 3.15 m/s

t1 + t2 = (3.15 m/s d + 5.93 m/s d) / (3.15 m/s)(5.93 m/s)

t1 + t2 = 9.08 m/s d / (3.15 m/s)(5.93 m/s)

The total traveled distance is 2 d and the total time is t1 + t2, so the average speed for the entire trip will be:

a.s = 2 · d / (t1 + t2)

a.s = 2 · d · ((3.15 m/s)(5.93 m/s) / 9.08 m/s d)

a.s = 4.11 m/s

The average speed is 4.11 m/s

b) The average velocity is calculated as the displacement over the elapsed time. The displacement is calculated as follows:

displacement = initial position - final position

In this case:

initial position = final position ( because Wilma returns to the starting point, there was no net displacement).

Then:

a.v = D/t

Where:

a.v = average velocity.

D = displacement

t = time.

a.v = 0/ t

a.v = 0

The average velocity is zero.

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explanation:

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