The average speed during any time interval is equal to the total distance of travel divided by the total time. Let d represent the distance between A and B. Let t1 be the time for which she has the higher speed of 5.15 m/s = d/t1. Let t2 represent the longer time for the return trip at 2.80 m/s =d/t2. Then the times are t1 = d/5.15 5.15 m/s and t2 = d/2.80 2.8 m/s. The average speed vavg is given by the following equation. vavg = Total distance/Total time = d + d/t1 + t2.

Average speed = 3.63 m/s

Explanation:

The average speed during any time interval is equal to the total distance travelled divided by the total time.

That is,

Average speed = distance/ time

Let d represent the distance between A and B.

Let t1 be the time for which she has the higher speed of 5.15 m/s. Therefore,

5.15 = d/t1.

Make d the subject of formula

d = 5.15t1

Let t2 represent the longer time for the return trip at 2.80 m/s . That is,

2.80 = d/t2.

Then the times are t1 = d/5.15 5 and

t2 = d/2.80.

The average speed vavg is given by the following equation.

avg speed = Total distance/Total time

Avg speed = d + d/t1 + t2

Where

Total distance = 2d

Total time = t1 + t2

Total time = d/5.15 + d/2.80

Total time = (2.8d + 5.15d)/14.42

Total time = 7.95d/14.42

Total time = 0.55d

Substitute total distance and time into the formula above.

Avg speed = 2d / 0.55d

Avg Speed = 3.63 m/s

no. dot product   =0 when vecs at right angles