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Vectors operations and uniform acceleration

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13. A bus travels at an average speed of 90 km/h. On average, how far does the bus travel in 20 min? Is this distance the magnitude of the actual displacement of the bus? Explain.

17. A student runs 30 m east, 40 m north, and 50 m west.

(a) The magnitude of the student's net displacement is (1) between 0 and 20 m, (2) between 20 m and 40 m, or (3) between 40 m and 60 m?
(b) What is his net displacement?
21. (a) Given that the speed of sound is 340 m / s and the speed of light is 3.00 X 10 m/s
(186 000 mi / s), how much time will elapse between a lightning flash and the resulting thunder if the lightning strikes 2.50 km away from the observer?
(b) Does your answer change if you assume the light travels with an infinite speed (i.e., the lightning flash is seen instantaneously)?

25. An earthquake releases two types of traveling waves, called "transverse" and "longitudinal." The average speeds of transverse and longitudinal seismic waves in rock are 8.9 km / s and 5.1 km / s, respectively. A seismograph records the arrival of the transverse waves 73 s before that that of the longitudinal waves. Assuming that the waves travel in straight lines, how far away is the center of the earthquake from the seismograph?

37. An automobile traveling at 25.0 km / h along a straight, level road accelerates to 65.0 km / h in 6.00 s. What is the magnitude of the auto's average acceleration?

55. The driver of a pickup truck going 100 km / h applies the brakes, giving the truck a
uniform deceleration of 6.50 m / s while it travels 20.0 m.

(a) What is the speed of the truck in kilometers per hour at the end of the distance?
(b) How much time has elapsed?

61. A bullet traveling horizontally at a speed of 350 m / s hits a board perpendicular to the surface, passes through it, and emerges on the other side at a speed of 210 m / s. If the board is 4.00 cm thick, how long does the bullet take to pass through it?

87. A stone is thrown vertically downward at an initial speed of 14 m / s from a height of 65 m above the ground.
(a) How far does the stone travel in 2.0 s?
(b) What is its velocity just before it hits the ground?

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The solution demonstrates what is the difference between distance and displacement and other issues regarding vectors arithmetics and uniform acceleration problems.

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