Average Velocity and Average Speed
5P. You drive on Interstate 10 from San Antonio to Houston, half the time at 55 krn/h and the other half at 90 km/h. On the way back you travel half the distance at 55 km/h and the other half at 90 km/h. What is your average speed (a) from San Antonio to Houston, (b) from Houston back to San Antonio, and (c) for the entire trip? (d) What is your average velocity for the entire trip?
(e) Sketch x versus t for (a), assuming the motion is all in the positive x direction. Indicate how the average velocity can be found on the sketch. Ilw
6P. Compute your average velocity in the following two cases (a) You walk 73.2 m at a speed of 1.22 m/s and then run 73.2 m at a speed of 3.05 m/s along a straight track. (b) You walk for 1.00 min at a speed of 1.22 m/s and then run for 1.00 min at 3.05 m/s along a straight track. (c) Graph x versus I for both cases and indicate how the average velocity is found on the graph.
7P. The position of an object moving along an x axis is given by x = 31 – 412 + t3, where x is in meters and I in seconds. (a) What is the position of the object at t = I, 2, 3, and 4 s? (b) What is the object’s displacement between t = 0 and t = 4 s? (c) What is its average velocity for the time interval from t = 2 s to t = 4 s? (d) Graph x versus t for 0 s t s 4 s and indicate how the answer
for (c) can be found on the graph. ssm www
8P. Two trains, each having a speed of 30 km/h, are headed at each other on the same straight track. A bird that can fly 60 km/h flies off the front of one train when they are 60 km apart and heads directly for the other train. On reaching the other train it flies directly back to the first train, and so forth. (We have no idea why a bird would behave in this way.) What is the total distance the bird travels?
9P. On two different tracks, the winners of the one-kilometer race ran their races in 2 min, 27.95 sand 2 min, 28. I5 s. In order to conclude that the runner with the shorter time was indeed faster, how much longer can the other track be in actual length? itw