# Distance, Displacement, speed, velocity, acceleration

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1 Problem 1 Distance, Displacement, speed, velocity, acceleration In the 2008 Olympics, Jamaican sprinter Usain Bolt shocked the world as he ran the 100-meter dash in 9.69 seconds. Determine Usain's average speed for the race. Sol: 10.3 m/s Problem 2 In the Funny Car competition at the Joliet Speedway in Joliet, Illinois in October of 2004, John Force completed the ¼-mile dragster race in a record time of seconds. Determine the average speed of the dragster in mi/hr and m/s. GIVEN: (1.000 mi =1609 m) Sol: mi/h and m/s Problem 3 In the qualifying round of the 50-yd freestyle in the sectional swimming championship, Dugan got an early lead by finishing the first yd in seconds. Dugan finished the return leg (25.00 yd distance) in seconds. a. Determine Dugan's average speed for the entire race. b. Determine Dugan's average speed for the first yd leg of the race. c. Determine Dugan's average velocity for the entire race. Sol: a) yd/s; b) yd/s; c) 0 yd/s. Problem 4 In last week's Homecoming victory, Al Konfurance, the star halfback of South's football team, broke a tackle at the line of scrimmage and darted upfield untouched. He averaged 9.8 m/s for an 80-yard (73 m) score. Determine the time for Al to run from the line of scrimmage to the end zone. Sol: 7.5 s Problem 5 During the annual shuffleboard competition, Renee gives her puck an initial speed of 9.32 m/s. Once leaving her stick, the puck slows down at a rate of m/s/s. a. Determine the time it takes the puck to slow to a stop. b. Use your initial speed and the calculated time to determine the distance which the puck travels before stopping. Sol: a) 2.30 s; b) 10.7 m Problem 6 Ken Runfast is the star of the cross-country team. During a recent morning run, Ken averaged a speed of 5.8 m/s for 12.9 minutes. Ken then averaged a speed of 6.10 m/s

2 for 7.1 minutes. Determine the total distance which Ken ran during his 20 minute jog. Sol: 7088 m Problem 7 A Formula One car is a single-seat racing car with an open cockpit and substantial wings located in the front and rear. At high speeds, the aerodynamics of the car help to create a strong downward force which allows the car to brake from 27.8 m/s (100 km/hr or 62.2 mi/hr) to 0 in as small of a distance as 17 meters. Determine the deceleration rate (i.e., acceleration) achieved by such a car. Sol: 22.7 m/s 2 Problem 8 Position Time; Velocity Time Graphs The position-time graph below represents the motion of South's basketball coach during the last sixteen seconds of overtime during this past weekend's game. Use the graph to answer the next several questions. a. Determine the total distance walked by the coach during these 16 seconds. b. Determine the resulting displacement of the coach during these 16 seconds. c. Determine the displacement of the coach after 12.0 seconds. d. At what time did the coach have the greatest displacement from his starting position? e. What was the fastest speed which the coach walked during any of the time intervals for the last 16.0 seconds? f. What was the average speed of the coach for these 16.0 seconds? Sol: a) 24 m ; b) 0 m; c) 6 m; d) 4-6 s and again at 14 s; e) 4 m/s; f) 1,5 m/s Problem 9 Mr. H is preparing to show the class a Strobe demonstration when he realizes that his absent-mindedness has struck once more. He left the strobe on the counter in the back

3 of the lab after the last class period. Starting 1.0 meter from the front of the room, Mr. H walks quickly to the back of the lab, picks up the strobe and returns to the middle of the classroom. The position-time graph below represents his motion. Use the graph to answer the next several questions. a. What is the total distance walked by Mr. H during these 8.0 seconds? S: 16 m b. What is the average speed of Mr. H during these 8.0 seconds? S: 2 m/s c. What is the average velocity of Mr. H during these 8.0 seconds? S: 0.5 m/s d. How fast did Mr. H walk during the first 5.0 seconds? S: 2 m/s e. How fast did Mr. H walk during the last 3.0 seconds? S: 2 m/s Problem 10 The position-time graph below represents the motion of two students - Mac (in red) and Tosh (in blue) - as they enter and exit the school library during a passing period.

4 Use the graph to determine the speeds at which the two students move. (Ignore any stationary periods of time.) Then determine how much faster the fastest student moves than the slower student. Sol: Mac s speed: 2,5 m/s; Tosh s speed: 4 m/s; Difference: 1,5 m/s Problem 11 Renatta Gas did it again. She failed to fill up her tank during the last four weeks. The velocity-time graph below represents the last six seconds of motion her car before being stranded on a highway in route to her university. Use this graph to determine... a. the acceleration of Renatta's car. Sol: - 3 m/s 2 b. the distance traveled during her last 6.0 seconds of motion. Sol: 54 m Problem 12 Marcus Tardee is driving his friends to school. With the start of school being only minutes away, he is unfortunately following a slow garbage truck. The truck finally turns down a side street and Marcus accelerates to a much more customary speed. The velocity-time graph below represents his motion. Use the graph to answer the following questions.

5 a. How fast was Marcus traveling while following the garbage truck? Sol: 4 m/s b. Determine the distance traveled during the first 4.0 seconds represented on the graph. Sol: 16 m c. Determine the acceleration of the car once the garbage truck turned onto the side street. Sol: 2.67 m/s 2 d. Determine the distance traveled by the car during the last 6.0 seconds of motion. Sol: 72 m Problem 13 After a long soccer practice down at the neighborhood soccer fields, Suzie begins walking up the steep hill towards her home. She gives her soccer ball a kick up the hill and continues walking towards it, meeting the ball as it is rolling back down. The velocity-time graph below depicts the motion of the ball. Use the graph to answer the following questions.

6 a. At what time did the ball change directions and begin rolling back down the hill? Sol: 3 s b. What is the acceleration of the ball as it rolls up the hill? down the hill? Sol: 4 m/s 2 c. How far up the hill did the ball roll before it began to roll back down? Sol: 18 m d. Determine the total distance traveled by the ball during the 5.00 seconds - both the distance up the hill and down the hill. Sol: 26 m e. How far up the hill did Suzie walk between the time when she kicked the ball and the time she met up with the ball (at 5.0 seconds)? Sol: 10 m Problem 14 Jeremy has recently taken up snowboarding as a hobby. He is practicing making smooth turns while traveling up sloped inclines. The velocity-time graph below depicts his motion traveling up an embankment and part-way down. Use the graph to answer the following questions. a. Determine Jeremy's acceleration at 8.0 seconds. Sol: - 2 m/s 2 b. Determine the distance Jeremy traveled from 0.0 to 5.0 seconds. Sol: 60 m c. At what time did Jeremy begin to travel back down the embankment? Sol: 11 s Problem 15 Rennata Gas is driving through town at 25.0 m/s and begins to accelerate at a constant rate of -1.0 m/s 2. Eventually Rennata comes to a complete stop. 1. Represent Rennata's accelerated motion by sketching a velocity-time graph. Use the velocity-time graph to determine this distance. 2. Use kinematic equations to calculate the distance that Rennata travels while decelerating. Sol: 312, 5 m

7 Problem 16 A Cessna 150 airplane has a takeoff speed of 28 m/s (63 mi/hr). a) Determine the minimum length of the runway which would be required for the plane to take off if it averages an acceleration of 1.9 m/s/s. Sol: 206 m b) How much time needs the airplane to take off? Sol: 14, 7 s Problem 17 Otto Emissions is driving his car at 25.0 m/s. Otto accelerates at 2.0 m/s 2 for 5 seconds. Otto then maintains a constant velocity for 10.0 more seconds. 1. Represent the 15 seconds of Otto Emission's motion by sketching a velocity-time graph. Use the graph to determine the distance that Otto traveled during the entire 15 seconds. 2. Finally, break the motion into its two segments and use kinematic equations to calculate the total distance traveled during the entire 15 seconds. Sol: 500 m Uniformly accelerated rectilinear motion (UARM) & Free Falling Problem 18 a) An airplane accelerates down a runway at 3.20 m/s 2 for 32.8 s until is finally lifts off the ground. Determine the distance traveled before takeoff. Sol: 1,720 m b) A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car. Sol: 8,10 m/s 2 Problem 19 a) Upton Chuck is riding the Giant Drop at Great America. If Upton free falls for 2.6 seconds, what will be his final velocity and how far will he fall? Sol: 33 m; 25,5 m/s b) A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. Determine the acceleration of the car and the distance traveled. Sol: 11,2 m/s 2 ; 79,8 m Problem 20 a) A feather is dropped on the moon from a height of 1.40 meters. The acceleration of gravity on the moon is 1.67 m/s 2. Determine the time for the feather to fall to the surface of the moon. Sol: 1,29 s b) A bike accelerates uniformly from rest to a speed of 7.10 m/s over a distance of 35.4 m. Determine the acceleration of the bike. Sol: 0,712 m/s 2

8 Problem 21 a) An engineer is designing the runway for an airport. Of the planes that will use the airport, the lowest acceleration rate is likely to be 3 m/s 2. The takeoff speed for this plane will be 65 m/s. Assuming this minimum acceleration, what is the minimum allowed length for the runway? Sol: 704 m b) A bullet leaves a rifle with a muzzle velocity of 521 m/s. While accelerating through the barrel of the rifle, the bullet moves a distance of m. Determine the acceleration of the bullet. Sol: 1, m/s 2 c) The observation deck of tall skyscraper 370 m above the street. Determine the time required for a penny to free fall from the deck to the street below. Sol: 8,7 s Problem 22 a) A bullet is moving at a speed of 367 m/s when it embeds into a lump of moist clay. The bullet penetrates for a distance of m. Determine the acceleration of the bullet while moving into the clay. (Assume a uniform acceleration.) Sol: - 1, m/s 2 b) A stone is dropped into a deep well and is heard to hit the water 3.41 s after being dropped. Determine the depth of the well. Sol: 57 m c) A plane has a takeoff speed of 88.3 m/s and requires 1365 m to reach that speed. Determine the acceleration of the plane and the time required to reach this speed. Sol: 2,86 m/s 2 & t = 30,8 s Problem 23 a) A dragster accelerates to a speed of 112 m/s over a distance of 398 m. Determine the acceleration (assume uniform) of the dragster. Sol: 15,8 m/s 2 b) With what speed must an object be thrown to reach a height of 91.5 m (equivalent to one football field)? Assume negligible air resistance. How long does the object take to reach that height? Sol: 42,35 m/s & 4,32 s Problem 24 Uniform Circular Motion During their physics field trip to the amusement park, Tyler and Maria took a rider on the Whirligig. The Whirligig ride consists of long swings which spin in a circle at relatively high speeds. As part of their lab, Tyler and Maria estimate that the riders travel through a circle with a radius of 6.5 m and make one turn every 5.8 seconds. Determine the speed of the riders on the Whirligig. Sol: 7 m/s

9 Problem 25 During the spin cycle of a washing machine, the clothes stick to the outer wall of the barrel as it spins at a rate as high as 1800 revolutions per minute. The radius of the barrel is 26 cm. a) Determine the speed of the clothes (in m/s) which are located on the wall of the spin barrel. Sol: 49 m/s b) Determine the acceleration of the clothes. Sol: 9, m/s 2 Problem 26 Elmira, New York boasts of having the fastest carousel ride in the world. The merry-goround at Eldridge Park takes riders on a spin at 18 mi/hr (8.0 m/s). The radius of the circle about which the outside riders move is approximately 7.4 m. a) Determine the time for outside riders to make one complete circle. Sol: 5,8 s b) Determine the acceleration of the riders. Sol: 8,7 m/s 2 Problem 27 A manufacturer of CD-ROM drives claims that the player can spin the disc as frequently as 1200 revolutions per minute. a) If spinning at this rate, what is the speed of the outer row of data on the disc; this row is located 5.6 cm from the center of the disc? Sol: 7 m/s b) What is the acceleration of the outer row of data? Sol: 8, m/s 2

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