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A car skids to a halt to avoid hitting an object in the road. Draw a basic motion diagram, using the images from the video, from the time the skid begins until the car is stopped? A rocket is launched straight up. Draw a basic motion diagram, using the images from the video, from the moment of liftoff until the rocket is at an altitude of 500 m? a. Write a paragraph describing the particle model. What is it, and why is it important? b. Give two examples of situations, different from those described in the text, for which the particle model... You drop a soccer ball from your third-story balcony. Use the particle model to draw a motion diagram showing the balls position and average velocity vectors from the time you release the ball until... A softball player slides into second base. Use the particle model to draw a motion diagram showing his position and his average velocity vectors from the time he begins to slide until he reaches the... a. FIGURE EX1.8 shows the first three points of a motion diagram. Is the objects average speed between points 1 and 2 greater than, less than, or equal to its average speed between points 0 and 1?... FIGURE EX1.10 shows two dots of a motion diagram and vector 1 Copy this figure, then add dot 3 and the next velocity vector 2 if the acceleration vector at dot 2 (a) Points up and (b) Points down.... Show a partial motion diagram. For each: a. Complete the motion diagram by adding acceleration vectors. b. Write a physics problem for which this is the correct motion diagram. Be imaginative! Dont... A regulation soccer field for international play is a rectangle with a length between 100 m and 110 m and a width between 64 m and 75 m. What are the smallest and largest areas that the field could... As an architect, you are designing a new house. A window has a height between 140 cm and 150 cm and a width between 74 cm and 70 cm. What are the smallest and largest areas that the window could be? A 5.4-cm-diameter cylinder has a length of 12.5 cm. What is the cylinders volume in SI units? An intravenous saline drip has 9.0 g of sodium chloride per liter of water. By definition, 1 mL = 1 cm 3 . Express the salt concentration in kg/m 3 ? The quantity called mass density is the mass per unit volume of a substance. What are the mass densities in SI units of the following objects? a. A 215 cm 3 solid with a mass of 0.0179 kg. b. 95 cm 3... FIGURE Q2.4 shows a position-versus-time graph for the motion of objects A and B as they move along the same axis. a. At the instant t = 1 s, is the speed of A greater than, less than, or equal to... Figure P1.58 shows a motion diagram of a car traveling down a street. The camera took one frame every 10 s. A distance scale is provided. Figure P1-58 a. Measure the x-value of the car at each dot.... For Questions 1 through 3, interpret the position graph given in each figure by writing a very short story of what is happening. Be creative! Have characters and situations! Simply saying that a car... FIGURE Q2.5 shows a position-versus-time graph for the motion of objects A and B as they move along the same axis. a. At the instant t = 1 s, is the speed of A greater than, less than, or equal to... FIGURE Q2.6 shows the position-versus-time graph for a moving object. At which lettered point or points: a. Is the object moving the slowest? b. Is the object moving the fastest? c. Is the object at... FIGURE Q2.7 shows the position-versus-time graph for a moving object. At which lettered point or points: (a) Is the object moving the fastest? (b) Is the object moving to the left? (c) Is the object... FIGURE Q2.8 shows six frames from the motion diagrams of two moving cars, A and B. (a) Do the two cars ever have the same position at one instant of time? If so, in which frame number (or numbers)?... Youre driving along the highway at a steady speed of 60 mph when another driver decides to pass you. At the moment when the front of his car is exactly even with the front of your car, and you turn... A bicycle is traveling east. Can its acceleration vector ever point west? Explain. A ball is thrown straight up into the air. At each of the following instants, is the magnitude of the balls acceleration greater than g, equal to g, less than g, or 0? Explain. a. Just after leaving... A rock is thrown (not dropped) straight down from a bridge into the river below. At each of the following instants, is the magnitude of the rocks acceleration greater than g, equal to g, less than g,... FIGURE EX2.7 is a somewhat idealized graph of the velocity of blood in the ascending aorta during one beat of the heart. Approximately how far, in cm, does the blood move during one beat? Figure Ex... FIGURE EX2.8 shows the velocity graph for a particle having initial position x 0 = 0 m at t 0 = 0 s. At what time or times is the particle found at x = 35 m? Figure Ex 2.8 V (m/s) 10- 5. 0- 2 4 6 -t... a. What constant acceleration, in SI units, must a car have to go from zero to 60 mph in 10 s? b. How far has the car traveled when it reaches 60 mph? Give your answer both in SI units and in feet. A jet plane is cruising at 300 m/s when suddenly the pilot turns the engines up to full throttle. After traveling 4.0 km, the jet is moving with a speed of 400 m/s. What is the jets acceleration,... FIGURE EX2.11 shows the velocity graph of a particle moving along the x-axis. Its initial position is x 0 = 2.0 m at t 0 = 0 s. At t = 2.0 s, what are the particles (a) Position, (b) Velocity, and... FIGURE EX2.12 shows the velocity-versus-time graph for a particle moving along the x-axis. Its initial position is x 0 = 2.0 m at t 0 = 0 s. a. What are the particles position, velocity, and... a. How many days will it take a spaceship to accelerate to the speed of light (3.0 10 8 m/s) with the acceleration g? b. How far will it travel during this interval? c. What fraction of a light year... When you sneeze, the air in your lungs accelerates from rest to 150 km/h in approximately 0.50 s. What is the acceleration of the air in m/s 2 ? A speed skater moving to the left across friction less ice at 8.0 m/s hits a 5.0-m-wide patch of rough ice. She slows steadily, then continues on at 6.0 m/s. What is her acceleration on the rough ice? A Porsche challenges a Honda to a 400 m race. Because the Porsches acceleration of 3.5 m/s 2 is larger than the Hondas 3.0 m/s 2 , the Honda gets a 1.0 s head start. Who wins? By how many seconds? A rock is tossed straight up from ground level with a speed of 20 m/s. When it returns, it falls into a hole 10 m deep. (a) What is the rocks velocity as it hits the bottom of the hole? (b) How long... A snowboarder glides down a 50-m-long, 15 o hill. She then glides horizontally for 10 m before reaching a 25 o upward slope. Assume the snow is friction less. a. What is her velocity at the bottom of... A small child gives a plastic frog a big push at the bottom of a slippery 2.0-m-long, 1.0-m-high ramp, starting it with a speed of 5.0 m/s. What is the frogs speed as it flies off the top of the ramp? FIGURE EX2.31 shows the acceleration-versus-time graph of a particle moving along the x-axis. Its initial velocity is v 0x = 8.0 m/s at t 0 = 0 s. What is the particles velocity at t = 4.0 s? Figure... FIGURE EX2.32 shows the acceleration graph for a particle that starts from rest at t = 0 s. What is the particles velocity at t = 6 s? Figure Ex 2.32 a, (m/s?) 10- 5- 0- -t (s) 2 The position of a particle is given by the function x = (2t 3 - 9t 2 + 12) m, where t is in s. a. At what time or times is v x = 0 m/s? b. What are the particles position and its acceleration at this... The position of a particle is given by the function x = (2t 3 6t 2 + 12) m, where t is in s. a. At what time does the particle reach its minimum velocity? What is (v x ) min ? b. At what time is the... Particles A, B, and C move along the x-axis. Particle C has an initial velocity of 10 m/s. In FIGURE P2.37, the graph for A is a position-versus-time graph; the graph for B is a velocity-versus time... A block is suspended from a spring, pulled down, and released. The blocks position-versus-time graph is shown in FIGURE P2.38. a. At what times is the velocity zero? At what times is the velocity... A particles velocity is described by the function v x = (t 2 - 7t + 10) m/s, where t is in s. a. At what times does the particle reach its turning points? b. What is the particles acceleration at... A particles velocity is described by the function v x = k t 2 m/s, where k is a constant and t is in s. The particles position at t 0 = 0 s is x 0 = - 9.0 m. At t 1 = 3.0 s, the particle is at x 1 =... A particles acceleration is described by the function a x = (10 t) m/s 2 , where t is in s. Its initial conditions are x 0 = 0 m and v 0x = 0 m/s at t = 0 s. a. At what time is the velocity again... A particles velocity is given by the function v x = (2.0 m/s) sin (pt), where t is in s. a. What is the first time after t = 0 s when the particle reaches a turning point? b. What is the particles... FIGURE P2.45 shows a set of kinematic graphs for a ball rolling on a track. All segments of the track are straight lines, but some may be tilted. Draw a picture of the track and also indicate the... Draw position, velocity, and acceleration graphs for the ball shown in FIGURE P2.44. See Problem 43 for more information. Figure P2.44 Vor A ball rolls along the smooth track shown in FIGURE P2.43. Each segment of the track is straight, and the ball passes smoothly from one segment to the next without changing speed or leaving the... The takeoff speed for an Airbus A320 jetliner is 80 m/s. Velocity data measured during takeoff are as shown. t (s) ___________ v x (m/s) 0 .. 0 10 .. 23 20 .. 46 30 .. 69 a. Is the jetliners... Two cars are driving at the same constant speed on a straight road, with car 1 in front of car 2. Car 1 suddenly starts to brake with constant acceleration and stops in 10 m. At the instant car 1... You are playing miniature golf at the golf course shown in FIGURE P2.51. Due to the fake plastic grass, the ball decelerates at 1.0 m/s 2 when rolling horizontally and at 6.0 m/s 2 on the slope. What... You are at a train station, standing next to the train at the front of the first car. The train starts moving with constant acceleration, and 5.0 s later the back of the first car passes you. How... A 200 kg weather rocket is loaded with 100 kg of fuel and fired straight up. It accelerates upward at 30 m/s 2 for 30 s, then runs out of fuel. Ignore any air resistance effects. a. What is the... A lead ball is dropped into a lake from a diving board 5.0 m above the water. After entering the water, it sinks to the bottom with a constant velocity equal to the velocity with which it hit the... A hotel elevator ascends 200 m with a maximum speed of 5.0 m/s. Its acceleration and deceleration both have a magnitude of 1.0 m/s 2 . a. How far does the elevator move while accelerating to full... A cheetah spots a Thomsons gazelle, its preferred prey, and leaps into action, quickly accelerating to its top speed of 30 m/s, the highest of any land animal. However, a cheetah can maintain this... A basketball player can jump to a height of 55 cm. How far above the floor can he jump in an elevator that is descending at a constant 1.0 m/s? You are 9.0 m from the door of your bus, behind the bus, when it pulls away with an acceleration of 1.0 m/s 2 . You instantly start running toward the still-open door at 4.5 m/s. a. How long does it... Ann and Carol are driving their cars along the same straight road. Carol is located at x = 2.4 mi at t = 0 h and drives at a steady 36 mph. Ann, who is traveling in the same direction, is located at... Amir starts riding his bike up a 200-m-long slope at a speed of 18 km/h, decelerating at 0.20 m/s 2 as he goes up. At the same instant, Becky starts down from the top at a speed of 6.0 km/h,... A very slippery block of ice slides down a smooth ramp tilted at angle . The ice is released from rest at vertical height h above the bottom of the ramp. Find an expression for the speed of the ice... Bob is driving the getaway car after the big bank robbery. Hes going 50 m/s when his headlights suddenly reveal a nail strip that the cops have placed across the road 150 m in front of him. If Bob... One game at the amusement park has you push a puck up a long, friction less ramp. You win a stuffed animal if the puck, at its highest point, comes to within 10 cm of the end of the ramp without... A motorist is driving at 20 m/s when she sees that a traffic light 200 m ahead has just turned red. She knows that this light stays red for 15 s, and she wants to reach the light just as it turns... Your goal in laboratory is to launch a ball of mass m straight up so that it reaches exactly height h above the top of the launching tube. You and your lab partners will earn fewer points if the ball... The two masses in FIGURE P2.75 slide on friction less wires. They are connected by a pivoting rigid rod of length L. Prove that v 2x = - v 1y tan θ. Figure P2.75 L. A sprinter can accelerate with constant acceleration for 4.0 s before reaching top speed. He can run the 100 meter dash in 10.0 s. What is his speed as he crosses the finish line? A rubber ball is shot straight up from the ground with speed v 0 . Simultaneously, a second rubber ball at height h directly above the first ball is dropped from rest. a. At what height above the... As an astronaut visiting Planet X, youre assigned to measure the free-fall acceleration. Getting out your meter stick and stop watch, you time the fall of a heavy ball from several heights. Your data... When a 1984 Alfa Romeo Spider sports car accelerates at the maximum possible rate, its motion during the first 20 s is extremely well modeled by the simple equation Where P = 3.6 à 10 4 watts... You are given the kinematic equation or equations that are used to solve a problem. For each of these, you are to: a. Write a realistic problem for which this is the correct equation(s). Be sure that... Careful measurements have been made of Olympic sprinters in the 100 meter dash. A quite realistic model is that the sprinters velocity is given by v x = a(1 - e -bt ) Where t is in s, v x is in m/s,... Can the magnitude of the displacement vector be more than the distance traveled? Less than the distance traveled? Explain. Can a vector have a component equal to zero and still have nonzero magnitude? Explain. Can a vector have zero magnitude if one of its components is nonzero? Explain. Suppose two vectors have unequal magnitudes. Can their sum be zero? Explain. The Starship Enterprise returns from warp drive to ordinary space with a forward speed of 50 km/s. To the crews great surprise, a Klingon ship is 100 km directly ahead, traveling in the same... You go to an amusement park with your friend Betty, who wants to ride the 30-m-diameter Ferris wheel. She starts the ride at the lowest point of a wheel that, as you face it, rotates... You are fixing the roof of your house when a hammer breaks loose and slides down. The roof makes an angle of 35 with the horizontal, and the hammer is moving at 4.5 m/s when it reaches the edge. What... Jack and Jill ran up the hill at 3.0 m/s. The horizontal component of Jills velocity vector was 2.5 m/s. a. What was the angle of the hill? b. What was the vertical component of Jills velocity? Kami is walking through the airport with her two-wheeled suitcase. The suitcase handle is tilted 40 from vertical, and Kami pulls parallel to the handle with a force of 120 N. (Force is measured in... Dee is on a swing in the playground. The chains are 2.5 m long, and the tension in each chain is 450 N when Dee is 55 cm above the lowest point of her swing. Tension is a vector directed along the... Your neighbor Paul has rented a truck with a loading ramp. The ramp is tilted upward at 25, and Paul is pulling a large crate up the ramp with a rope that angles 10 above the ramp. If Paul pulls with... Tom is climbing a 3.0-m-long ladder that leans against a vertical wall, contacting the wall 2.5 m above the ground. His weight of 680 N is a vector pointing vertically downward. (Weight is measured... A flock of ducks is trying to migrate south for the winter, but they keep being blown off course by a wind blowing from the west at 6.0 m/s. A wise elder duck finally realizes that the solution is to... A cart that is rolling at constant velocity on a level table fires a ball straight up. a. When the ball comes back down, will it land in front of the launching tube, behind the launching tube, or... Anita is running to the right at 5 m/s in FIGURE Q4.8. Balls 1 and 2 are thrown toward her by friends standing on the ground. According to Anita, both balls are approaching her at 10 m/s. Which ball... Zack is driving past his house in FIGURE Q4.10. He wants to toss his physics book out the window and have it land in his driveway. If he lets go of the book exactly as he passes the end of the... In FIGURE Q4.11, Yvette and Zack are driving down the freeway side by side with their windows down. Zack wants to toss his physics book out the window and have it land in Yvettes front seat. Ignoring... In uniform circular motion, which of the following quantities are constant: speed, instantaneous velocity, the tangential component of velocity, the radial component of acceleration, the tangential... FIGURE Q4.13 shows three points on a steadily rotating wheel. a. Rank in order, from largest to smallest, the angular velocities Ï 1 , Ï 2 , and Ï 3 of these points. Explain. b. Rank... In the Olympic shot-put event, an athlete throws the shot with an initial speed of 12.0 m/s at a 40.0 angle from the horizontal. The shot leaves her hand at a height of 1.80 m above the ground. How... A supply plane needs to drop a package of food to scientists working on a glacier in Greenland. The plane flies 100 m above the glacier at a speed of 150 m/s. How far short of the target should it... You have a remote-controlled car that has been programmed to have velocity where t is in s. At t = 0 s, the car is at What are the cars (a) Position vector and (b) Acceleration vector at t = 2.0 s?... Mary needs to row her boat across a 100-m-wide river that is flowing to the east at a speed of 1.0 m/s. Mary can row with a speed of 2.0 m/s. a. If Mary points her boat due north, how far from her... FIGURE EX4.23 shows the angular-velocity-versus-time graph for a particle moving in a circle. How many revolutions does the object make during the first 4 s? Figure Ex 4.23 w (rad/s) 20- 10- t (s) 0-... FIGURE EX4.24 shows the angular-position-versus-time graph for a particle moving in a circle. What is the particles angular velocity at (a) t = 1 s, (b) t = 4 s, and (c) t = 7 s? Figure Ex 4.24 0... FIGURE EX4.25 shows the angular-velocity-versus-time graph for a particle moving in a circle, starting from θ 0 = 0 rad at t = 0 s. Draw the angular-position-versus-time graph. Include...
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