Unit 1: Uniform Motion Name Speed and Velocity Problems. Show every step and report all answers with appropriate units. 1. What is the average speed of a cheetah that sprints 100 m in 4 s? 2. How about if it sprints 50 m in 2 s? 3. If a car moves with an average speed of 60 km/hr for an hour, it will travel a distance of 60 km. How far will it travel if it continues this average rate for 4 hrs? 4. A runner makes one lap around a 200 m track in a time of 25.0 s. What was the runner's average speed? Answer: 8.0 m/s. Show me how you get this answer.
5. Light and radio waves travel through a vacuum in a straight line at a speed of very nearly 3.00 10 8 m/s. How far is light year (the distance light travels in a year)? Answer: 9.50 10 15 m. Show me how you get this answer. 6. A motorist travels 406 km during a 7.0 hr period. What was the average speed in km/hr and m/s? Answers: 58 km/hr, 16 m/s. 7. A bullet is shot from a rifle with a speed of 720 m/s. What time is required for the bullet to strike a target 3240 m away? Answer: 4.5 s. 8. Light from the sun reaches the earth in 8.3 minutes. The speed of light is 3.0 10 8 m/s. In kilometers, how far is the earth from the sun? Answer: 1.5 10 8 km.
9. *An auto travels at a rate of 25 km/hr for 4 minutes, then at 50 km/hr for 8 minutes, and finally at 20 km/hr for 2 minutes. Find the total distance covered in km and the average speed for the complete trip in m/s. Answers: 9 km, 10.7 m/s. 10. *If you traveled one mile at a speed of 100 miles per hour and another mile at a speed of 1 mile per hour, your average speed would not be (100 mph + 1 mph)/2 or 50.5 mph. What would be your average speed? (Hint: What is the total distance and total time?) Answer: 1.98 mph. 11. *What is your average speed in each of these cases? a. You run 100 m at a speed of 5.0 m/s and then you walk 100 m at a speed of 1.0 m/s. b. You run for 100 s at a speed of 5.0 m/s and then you walk for 100 s at a speed of 1.0 m/s. Answers: 1.7 m/s, 3.0 m/s. 12. *A race car driver must average 200 km/hr for four laps to qualify for a race. Because of engine trouble, the car averages only 170 km/hr over the first two laps. What average speed must be maintained for the last two laps?
13. *A car traveling 90 km/hr is 100 m behind a truck traveling 50 km/hr. How long will it take the car to reach the truck? 14. The peregrine falcon is the world's fastest known bird and has been clocked diving downward toward its prey at constant vertical velocity of 97.2 m/s. If the falcon dives straight down from a height of 100. m, how much time does this give a rabbit below to consider his next move as the falcon begins his descent?
More Speed and Velocity Problems 15. Hans stands at the rim of the Grand Canyon and yodels down to the bottom. He hears his yodel back from the canyon floor 5.20 s later. Assume that the speed of sound in air is 340.0 m/s. How deep is the canyon? 16. The horse racing record for a 1.50 mi. track is shared by two horses: Fiddle Isle, who ran the race in 143 s on March 21, 1970, and John Henry, who ran the same distance in an equal time on March 16, 1980. What were the horses' average speeds in: a. mi/s? b. mi/hr? 17. For a long time it was the dream of many runners to break the "4-minute mile." Now quite a few runners have achieved what once seemed an impossible goal. On July 2, 1988, Steve Cram of Great Britain ran a mile in 3.81 min. During this amazing run, what was Steve Cram's average speed in: a. mi/min? b. mi/hr?
18. It is now 10:29 a.m., but when the bell rings at 10:30 a.m. Suzette will be late for French class for the third time this week. She must get from one side of the school to the other by hurrying down three different hallways. She runs down the first hallway, a distance of 35.0 m, at a speed of 3.50 m/s. The second hallway is filled with students, and she covers its 48.0 m length at an average speed of 1.20 m/s. The final hallway is empty, and Suzette sprints its 60.0 m length at a speed of 5.00 m/s. a. Does Suzette make it to class on time or does she get detention for being late again? b. Draw a distance vs. time graph of the situation. (Assume constant speeds for each hallway.) 19. During an Apollo moon landing, reflecting panels were placed on the moon. This allowed earthbased astronomers to shoot laser beams at the moon's surface to determine its distance. The reflected laser beam was observed 2.52 s after the laser pulse was sent. The speed of light is 3.0 10 8 m/s. What was the distance between the astronomers and the moon? 20. For many years, the posted highway speed limit was 88.5 km/hr (55 mi/hr) but in recent years some rural stretches of highway have increased their speed limit to 104.6 km/hr (65 mi/hr). In Maine, the distance from Portland to Bangor is 215 km. How much time can be saved in making this trip at the new speed limit?
21. The tortoise and the hare are in a road race to defend the honor of their breed. The tortoise crawls the entire 1000. m distance at a speed of 0.2000 m/s while the rabbit runs the first 200.0 m at 2.000 m/s The rabbit then stops to take a nap for 1.300 hr and awakens to finish the last 800.0 m with an average speed of 3.000 m/s. Who wins the race and by how much time? 22. Two physics professors challenge each other to a 100. m race across the football field. The loser will grade the winner's physics labs for one month. Dr. Rice runs the race in 10.40 s. Dr. De La Paz runs the first 25.0 m with an average speed of 10.0 m/s, the next 50.0 m with an average speed of 9.50 m/s, and the last 25.0 m with an average speed of 11.1 m/s. Who gets stuck grading physics labs for the next month?