Linear Motion

Examples of solutions

Problem 1

A rocket carrying a satellite is accelerating straight up from the earth's surface. At 1.35 s after liftoff, the rocket clears the top of its launch platform, 63 m above the ground. After an additional 4.45 s it is 1.00 km above the ground. Calculate the magnitude of the average velocity of the rocket for a) the 4.45-s part of its flight; b) the first 5.80 s of its flight.

Problem 2

A hiker travels in a straight line for 40 min with an average velocity that has magnitude 1.2 m/s. How far is she from her starting point after this time?

Problem 3

You normally drive on the freeway between San Francisco and Sacramento at an average speed of 96 km/h (60 mi/h), and the trip takes 2 h and 10 min. On a rainy day you decide to slow down and drive the same distance at an average speed of 80 km/h (50mi/h). How much longer does the trip take?

Problem 4

In an experiment, a shearwater (a seabird) was taken from its nest,flown 5150 km away, and released. It found its way back to its nest 12.5 days after it was released. If we place the origin at the nest and extend the +x-axis to the release point, what was the bird's average velocity for
a) the return flight?
b) the whole episode, from leaving the nest to returning?

Problem 5

Your old VW van sputters along at an average speed of 8.0 m/s for 60 s, then catches hold and zips along at an average speed of 24.0 m/s for another 60 s.
a) Calculate your average speed for the entire 120 s.
b) Suppose the speed of 8.0 m/s was maintained while you traveled 480 m, followed by the average speed of 24.0 m/s for another 480 m. Calculate your average speed for the entire distance.
c) In which case is the average speed for the entire motion the numerical average of the two speeds?

Problems for solution without assistance

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