Question

Homework 2

Show all work done for calculations, starting with an equation whenever possible, and include all units. If asked to explain, give a brief response (1-2 complete sentences). A sightseer takes a trip in her car, making three stops; each leg of the journey is 150 km. During the first leg, she drives at an average speed of 50 km/hr. With better roads and lighter traffic, she drives at an average speed of 75 km/hr for the second leg. But on the third leg, traffic and roads are horrible, and her average speed is only 30 km/hr.

a) Calculate the average of her three average speeds, and then calculate her overall average speed for the entire journey.

b) In physical (rather than mathematical) terms, why is her overall average speed less than the average of the three average speeds? Explain without further calculations.

c) For the moment, assume that she traveled in a straight line from start to finish, and that she traveled at a constant speed during each leg. Under these assumptions, sketch an x vs. t graph for her journey, and also sketch a line whose slope would be equal to her overall average speed. Label the lines on the graph “1”, “2”, “3” for the legs and “savg” for the final line. Graph paper is not required, but you should use a ruler and mark off proportional ticks on each axis (e.g., 0 km, 50 km, 100 km, etc. for the x axis; 1 hr, 2 hr, etc. for the t axis).

d) Forget the assumptions made in (c), now. Let's say that it turns out that her average velocity for the trip was vavg = 25 km/hr. What can you deduce about her trip from this additional information? Show all work and explain.

Answer 1

given

three stops in the journey

each leg of journey , d = 150 km

v1 = 50km/hr

v2 = 75 km/hr

v3 = 30 km/hr

a. average speed = total distance/total time

vav = (3d)/d(1/v1 + 1/v2 + 1/v3)

vav = 45 km/hr

b. her overall speed is less than the average of her speeds because the three legs dont take same time to cover, hence theore average will not be average speed

c. following is the graph

d. vavg = 25 km/hr

total distance = 150 km

hence

total time = t

25 = 150/t

t = 6 hours