One-Dimensional Kinematics Unit 1 One-Dimensional Kinematics

Working Problems (It is the same format you saw in math.) Step 1—Read the problem. Draw a diagram, if needed. Step 2—Determine the appropriate equation(s) Step 3—Substitute the letters with numbers Step 4—Solve the problem, don’t forget the correct units Chapter 2 One-Dimensional Kinematics 2

Problem Format (in PP) Problem

Problem Format (on Tests)

Scoring (on Quiz & Tests) Correct Equation 2 points Correct Substitution 2 points Correct Units ½ point Correct Numerical Answer ½ point NOTE: You should be able to earn 4 ½ points without your calculator Chapter 2 One-Dimensional Kinematics 5

Chapter 2 One-Dimensional Kinematics Emphasis Lecture & Quizzes  The emphasis will be on the set-up, the substitution, and the units for the answer. I am assuming that you can calculate the numerical answer if you have correctly completed the first two steps Chapter 2 One-Dimensional Kinematics 6

Reporting Your Numerical Answer Remember the smaller the number, the more decimal places you need. The problem does help you determine how you need to report your answer. Be reasonable when reporting your answer. You don’t need to go “overboard” with the number of decimal places. If you are comfortable with significant digits, 3 or 4 sig figs are sufficient. Chapter 2 One-Dimensional Kinematics 7

Chapter 2 One-Dimensional Kinematics Example #1 You travel 4.0 km west and then 12.0 km north. What is the distance traveled? Chapter 2 One-Dimensional Kinematics 8

Chapter 2 One-Dimensional Kinematics Example #2 You travel 4.0 km west and then 12.0 km north. What is the displacement traveled? Chapter 2 One-Dimensional Kinematics 9

Chapter 2 One-Dimensional Kinematics Example Problem #3 You travel a certain distance east and then turn south for 20.0 km until you are 50.0 km from home. What is the displacement traveled? What is the distance traveled? Chapter 2 One-Dimensional Kinematics 10

Chapter 2 One-Dimensional Kinematics Know Thy Units Velocity (speed)  meters/second (m/sec) Distance  meters (m) Time  seconds (sec) Acceleration  meters/second2 (m/sec2 ) Chapter 2 One-Dimensional Kinematics 11

Chapter 2 One-Dimensional Kinematics Equation de jour Chapter 2 One-Dimensional Kinematics 12

Example #1 An athlete sprints 50.0 m in 8.00 seconds. What is the average sprint velocity?

Example #3 The athlete walks back to the starting line in at a time of 40.00 seconds. What is the average walking velocity?

Example #4 Radio waves travel at the speed of light (186000 mi/sec) How long does it take for a radio message to travel from the Earth to the moon and back?

Example #4 A runner can complete a 450 meter straight line course in 55.65 seconds. What is the runner’s velocity?

Chapter 2 One-Dimensional Kinematics Equation de jour Chapter 2 One-Dimensional Kinematics 17

Example #1 A car goes from 0 to 26.8 m/sec in 12.00 seconds. What is its average acceleration?

Example #2 A ferry, traveling in the positive x direction at a speed of 7.4 m/sec, slows to a stop in 12.30 seconds. What is its average acceleration?

Example #3 The ferry, traveling in the negative x direction at a speed of 7.3 m/sec, slows to a stop in 13.10 seconds. What is its average acceleration?

Example #4 A jet makes a landing traveling due east with a speed of 115 m/sec. If the jet comes to rest in 13.00 seconds, what is the magnitude and direction of its average acceleration?

Example #5 A 747 airliner reaches its takeoff speed of 73.0 m/sec in 35.2 seconds. What is the magnitude of its acceleration?

Example #6 A boat moves at a speed of 1.50 m/sec. It then accelerates at 2.40 m/sec2. What is its speed after 5.00 seconds?

Example #7 A boat moves at a speed of 1.50 m/sec. It accelerates at 2.50 m/sec2. How much time does it take the boat to have a speed of 10.00 m/sec?

Example #8 A runner will accelerate at 1.9 m/sec2 for 5.2 seconds from her starting position. What is her speed at 2.00 seconds?

Example #9 A car is traveling due north at 18.1 m/sec. What is the car’s velocity after 7.50 seconds if its acceleration is 1.30 m/sec2 due north?

Example #10 A car is traveling due north at 18.1 m/sec. What is the cart’s velocity after 7.50 seconds if the car’s acceleration is 1.15 m/sec2 due south?

Example #11 A particle has an acceleration of 6.24 m/sec2 for 0.30 seconds. At the end of this time, the particle’s velocity is 9.31 m/sec. What was the particle’s initial velocity?

Chapter 2 One-Dimensional Kinematics Equation de jour Chapter 2 One-Dimensional Kinematics 29

Example #1 A boat has a speed of 1.50 m/sec. It accelerates at 2.40 m/sec2 for 5.00 seconds. What is the distance traveled during this time?

Example #2 A drag racer starts from rest and accelerates at 7.40 m/sec2 for 2.00 seconds. What is the distance covered during this time?

Example #3 A child slides down an ice-covered hill at an acceleration of 1.8 m/sec2. If the child starts from rest, how far does he travel in 3.00 seconds?

Example #4 You are driving at 16 m/sec. If you apply the brakes and decelerate at a rate of 3.2 m/sec2, how much time does it take to travel 25 m?

Example #5 A runner is at the 100 m mark in a race. Her rate is 2.5 m/sec. She then accelerates at 3.5 m/sec2 for 4.00 seconds. What is her position in the race?

Example #6 Your position is at the 1500 m mark on a course and your are traveling at 10.8 m/sec. You then accelerate at -2.5 m/sec2 for 10.00 seconds. What is your new position?

Example #7 You can travel at 25.8 m/sec. You then accelerate at 4.7 m/sec2 for a distance of 300 m. How much time did it take to travel that distance?

Chapter 2 One-Dimensional Kinematics Equation de jour Chapter 2 One-Dimensional Kinematics 37

Example #1 A car, traveling at 10.0 m/sec, accelerates at 1.5 m/sec2 for a distance of 60.0 m. What is the new speed of the car?

Example #2 An object accelerates from rest at 3.54 m/sec2. What is the object’s speed after it has covered a distance of 150 m?

Example #3 A car can accelerate at a rate of -2.54 m/sec2 when coming to a stop. If the skid marks measure 46.5 m, what was the car’s initial velocity?

Example #4 A rock, traveling at 130 m/sec stops in 22 cm. What was the acceleration of the rock?

Example #5 A car traveling at 8.4 m/sec slows down to 6.4 m/sec in 7.2 m. What is the car’s acceleration?

Chapter 2 One-Dimensional Kinematics Vertical Motion The same equations can be used for objects in vertical motion. Just remember that g = 10 m/sec2 (can be positive or negative, depending upon circumstances) Chapter 2 One-Dimensional Kinematics 43

Example #1 Gulls are often observed dropping clams from a height of 14 m in order to break the shell. How fast is the shell moving when it hits the rocks?

Example #2 A volcano launches a lava bomb straight upward with an initial speed of 28 m/sec. Find the velocity 2.00 seconds after launch?

Example #3 A volcano on Io ejected material to a height of 200000 m. What is the initial velocity of the material if g on Io is 1.8 m/sec2?

Example #4 A swimmer jumps off a bridge and lands in the water 1.5 seconds later. How high is the bridge?

Example #5 A softball player throws the ball upward with a velocity of 20.0 m/sec. How much time does it take for the ball to reach the player?

Example #6 An astronaut on the Moon drops a rock downward from a height of 1.25 m. If the acceleration of gravity on the Moon is 1.62 m/sec2, what is the speed of the rock just before it it’s the ground?

Chapter 2 One-Dimensional Kinematics Position-time Graph x t Chapter 2 One-Dimensional Kinematics 50

Chapter 2 One-Dimensional Kinematics Position-time Graph x t Chapter 2 One-Dimensional Kinematics 51

Chapter 2 One-Dimensional Kinematics Velocity-time Graph v t Chapter 2 One-Dimensional Kinematics 52

Chapter 2 One-Dimensional Kinematics Velocity-time Graph v t Chapter 2 One-Dimensional Kinematics 53

Laboratory Exercises Velocity of a Rolling Golf Ball Dropping Golf Balls 2 Determine “g” with an Inclined Plane What is Your Reaction Time?

Review Time

Name that equation #1 A motorist drives 150 km from one city to another in 2.5 hours. What is the average speed for the trip? 56

Name that equation #2 If a dropped object falls for 2.00 seconds, how far did it fall? 57

Name that equation #3 A rock hits the ground at a speed of 10 m/sec and leaves a hole 25 cm deep. What is the magnitude of the deceleration of the rock? 58

Name that equation #4 A motorboat traveling in a straight course slows down uniformly from 75 km/hr (20.8 m/sec) to 40 km/hr (11.1 m/sec) in a distance of 50 m. What is the acceleration? 59

Name that equation #5 A ball is projected vertically downward at a speed of 4.0 m/sec. How far does the ball travel in 1.80 seconds? 60

Name that equation #6 A skier with speed of 5.0 m/sec crests a hill. On the downslope, she accelerates at 3.0 m/sec2 for 3.5 seconds. What is her final speed? 61

Name that equation #7 At what speed must an object be projected vertically upward for the object to reach a maximum height of 14.0 m above its starting point? 62

Name that equation #8 At a sports car rally, a car starting from rest accelerates uniformly at a rate of 9.0 m/sec2 over a straight-line distance of 100 m. How much time does this take? 63

Name that equation #9 A rocket car is traveling at a constant speed of 250 km/hr (69.4 m/sec). The driver gives the car a reverse thrust and in experiences a constant deceleration of 8.25 m/sec2. How much time elapses for the car to travel 175 m? 64

Name that equation #10 A jet aircraft being launched from an aircraft carrier is accelerated at 4.5 m/sec2 from rest along a 94 m track for 2.5 seconds. What is the launch speed of the jet? 65