Problems:

Speed and Velocity

6-1. A car travels a distance of 86 km at an average speed of 8 m/s. How many hours were required for the trip? [pic] [pic] t = 2.99 h

6-2. Sound travels at an average speed of 340 m/s. Lightning from a distant thundercloud is seen almost immediately. If the sound of thunder reaches the ear 3 s later, how far away is the storm? [pic] t = 58.8 ms

6-3. A small rocket leaves its pad and travels a distance of 40 m vertically upward before returning to the earth five seconds after it was launched. What was the average velocity for the trip? [pic] v = 16.0 m/s

6-4. A car travels along a U-shaped curve for a distance of 400 m in 30 s. It’s final location, however is only 40 m from the starting position. What is the average speed and what is the magnitude of the average velocity? Average speed: [pic] v = 13.3 m/s

Average velocity: [pic] v = 1.33 m/s, E

6-5. A woman walks for 4 min directly north with a average velocity of 6 km/h; then she walks eastward at 4 km/h for 10 min. What is her average speed for the trip? t1 = 4 min = 0.0667 h; t2 = 10 min = 0.167 h

s1 = v1t1 = (6 km/h)(0.0667 h) = 0.400 km

s1 = v2t2 = (4 km/h)(0.167 h) = 0.667 km

[pic] v = 4.57 km/h

6-6. What is the average velocity for the entire trip described in Problem 6-5? [pic] D = 0.778 km, 31.00

[pic] v = 3.33 km/h, 31.00

6-7. A car travels at an average speed of 60 mi/h for 3 h and 20 min. What was the distance?

t = 3 h + 0.333 h = 3.33 h; s = vt = (60 mi/h)(3.33 h); s = 200 mi

6.8 How long will it take to travel 400 km if the average speed is 90 km/h? [pic] t = 4.44 h

*6-9. A marble rolls up an inclined ramp a distance of 5 m, then stops and returns to a point 5 m below its starting point. The entire trip took only 2 s. What was the average speed and what was the average velocity? (s1 = 5 m, s2 = -10 m) speed = [pic] v = 7.50 m/s

velocity = [pic] v = – 2.5 m/s, down plane.

Uniform Acceleration

6-10. The tip of a robot arm is moving to the right at 8 m/s. Four seconds later, it is moving to the left at 2 m/s. What is the change in velocity and what is the acceleration. (v = vf - vo = (–2 m/s) – (8 m/s) (v = –10 m/s

[pic] a = –2.50 m/s2

6-11. An arrow accelerates from zero to 40 m/s in the 0.5 s it is in contact with the bow string. What is the average acceleration? [pic] a = 80.0 m/s2

6-12. A car traveling initially at 50 km/h accelerates at a rate of 4 m/s2 for 3 s. What is the final speed? vo = 50 km/h = 13.9 m/s; vf = vo + at

vf = (13.9 m/s) + (4 m/s2)(3 s) = 25.9 m/s; vf = 25.9 m/s

6-13. A truck traveling at 60 mi/h brakes to a stop in 180 ft. What was the average acceleration and stopping time? vo = 60 mi/h = 88.0 ft/s 2as = vf2 – vo2

[pic] a = – 21.5 ft/s2

[pic] t = 4.09 s

6-14. An arresting device on a carrier deck stops an airplane in 1.5 s. The average acceleration was 49 m/s2. What was the stopping distance? What was the initial speed? vf = vo + at; 0 = vo + (– 49 m/s2)(1.5 s); vo = 73.5 m/s s = vf t - ½at2 ; s = (0)(1.5 s) – ½(-49 m/s2)(1.5 s)2; s = 55.1 m 6-15. In a braking test, a car traveling at 60 km/h is stopped in a time of 3 s. What was the acceleration and stopping distance? ( vo = 60 km/h = 16.7 m/s) vf = vo + at; (0) = (16.7 m/s) + a (3 s); a = – 5.56 m/s2 [pic]; s = 25.0 m

6-16. A bullet leaves a 28-in. rifle barrel at 2700 ft/s. What was its acceleration and time in the barrel? (s = 28 in. = 2.33 ft) 2as = vo2 - vf2 ; [pic]; a = 1.56 x 106 m/s2

[pic]; t = 1.73 ms

6-17. The ball in Fig. 6-13 is given an initial velocity of 16 m/s at the bottom of an inclined plane. Two seconds...