1. What is a tangent line and what is it used for? Sketch an example. 2. What value is the slope of a v vs t graph for a free-falling object? Why? 3. If wind resistance was included in the previous question, would the slope get bigger or smaller? 4. Describe the Apollo 15 experiment involving the hammer and feather. Explain why this doesn't work on Earth. 5. What is the acceleration shown in the following graph? Velocity vs. Time 40 30 Velocity (m/s [forward]) 10 Time (s) 6. Sketch d vs t and v vs t graphs for a stone that was dropped off a 30 m cliff. Just the rough shape and highlights is good. 7. Sketch d vs t and v vs t graphs for a stone that was thrown upwards at 5 m/s. Just the rough shape and highlights is good.Answers: Intro to Kinematics: 1) magnitude, magnitude, direction 2) straight line 3) Less 4) V: displacement, force, 20m/s[N], velocity, 50m[down], 9.8m/s2[down], acceleration, 10km[SW] S: 1kg, 10km/hr, distance, 200km, 5hours, 40L, mass, speed 7) change 8) 10,0,15,-5,-10,5 9)1km[N] 10)0.5m[S] 11)+3.5m 12)58m[31 WofN] or 58m[59 NofW] 13)600.km, 447[27 WofN] Velocity 4)2.7m/s[E] 5)91[W] 6)30.s 8)21m/s 9)70km/h 10)35km/h,9.6m/s 11)40.km[E] 12)+5m, +2m/s Graphing Motion: Ba) no, y-intercepts are different b) B c) A d) A has a steeper slope e) A and B are at the same position 4)2.5s,5s,20m, 10m,4m/s,2m/s 5) a) Os,32s,55s b) 15-20s c) 20-40s d) 4m/s, 5m/s e) 3m/s f)0, 3.6m/s 6. The ball doesn't move at first. Then it moves backwards and then finally stops. position thiri 7 . Time (al 8. Timeis 9. Acceleration: 5)m, s, m/s, m/s2 6)11m/s 7)7m/s 8)4.0s 12)0.82s 14)23m/s[down] 15) pos, neg, neg, pos, pos 17) a)pos, inc, pos b) neg, dec, neg c) pos, dec, neg d) neg, inc, pos 18) velocity, velocity Graphing with Acceleration: 5)12.5m/s2 6/7)parabola, linear 8)a)perhaps at 0 minutes b)0,30,55min c)30-55min d)60m/min,6m/min2 9)50m 10)50m Problem Solving 1) 77.5 m/s2 2) a=0.278m/s2 3) 1.44x105 m 4) 80.s 5)2470m 6)0.87m/s2 [opposite] 7)2.9 s 8)80s 9)1.65s 10)53.3km/h or 14.8m/s 11)115m 12)0.625h, 133km/h 13) 225m 14) 6.3m/s[right] 15)0.46m/s2 16)59m/s[down] 17)5.0m/s2 18)4.0m/s 19)250m 20)0.94m/s 21)2x105 m/s2 22)30.6m/s 23)5.0m/s6. How long would it take a polar bear walking north at 0.80 m/s to travel 24 m north? Show the equation used and all steps. 7. Describe what a negative velocity indicates and provide an example. 8. Convert 75 km/hr to m/s. Show all steps. 9. Convert 20 m/s to km/hr. Show all steps. 10. A truck's displacement is 45 km north after driving for 1.3 h. What was the truck's average velocity in km/h and m/s? Show the equation used and all steps. 11. What is the displacement of an airplane flying 480 km/h [E] during a 5.0 min time interval? Show the equation used and all steps. 12. What is Tony Hawk's displacement and velocity between 2 and 5 seconds? = 0s t= 2s t = 5s m 1m 2m 3m 4m 5m 6m 7m 8m10. 11. 12. 13. A toboggan accelerates from rest at 1.1 misE. After 10. seconds, how fast is it going? Show the equation used and all steps. At the bottom of the hill, the toboggan moving 12 mfs forward accelerates at -0.50 mls2 for 10 5. What is the toboggan's velocity at the end of the 10 5? Show the equation used and all steps. How much time does it take a car travelling south at 12 ms to increase its velocity to 26mls south if it accelerates at 3.5 mls2 south? Show the equation used and all steps. The acceleration of a freely falling object (near Earth), when we assume no air resistance, is {remember units). The assumption of no air resistance is never totally true but is often close enough to make pretty accurate calculations. Discuss the properties of free-falling masses where this is a really good assumption and when it isn't. An apple falls from a tree heading directly for Newton's head. What is its velocity after 1 second? After 2 seconds? A ball is thrown straight up into the air at 14 mils. How long does it take for the ball to slow down to an upward velocity of6.0 mis? Show the equation used and all steps. If you throw a rock up into the air, when is its velocity zero? What is the acceleration when the velocity is zero? 1. In 2019, Sammy Miller drove a rocket powered dragster from rest to 402m (1/4 mile) in a record 3.22s. What acceleration did he experience? 2. If a car is going 100. km/hr as it passes a bystander, then passes another bystander 20.0 seconds later when it's going 120. km/hr, what is the car's average acceleration? Show all work as demonstrated in the lessons. 3. A submarine is travelling at a constant velocity of 20.0 m/s for 2.00 hours. What distance did it travel? Show all work as demonstrated in the lessons. 4. A stationary boat accelerates to 90. km/hr over 1.0 km. What is the time it takes to do this? Show all work as demonstrated in the lessons. 5. A braking train can decelerate at 0.400 m/s2. If the train is travelling at 160. km/hr and needs to plan to stop at a pick-up area. How far in advance does it need to apply the brakes? Show all work as demonstrated in the lessons.4. The motion of two runners is graphed below (Alasie and Brent). Position vs. Time a) How long did each runner take to reach 10 meters? jogger A jogger B Position (m [forward]) b) What was the distance each traveled in the first 5 seconds? 6 7 8 9 c) Determine the speed of each runner. Show all work. 5. The motion of a race car on a linear track is shown below. a) When is the car at the starting line? 80 60 40 b) When is the car sitting still? 20 displacement (m) time (s) c) When is the car going in the -20 negative direction? .40 10 20 30 d) What is the biggest velocity logged? What is the biggest speed? Show all work. e) What is the average velocity of the car between 0 and 20 seconds? Show all work. What is the average velocity of the car for the entire trip? Average Speed? Show all work .11. A car starts at rest and after 9.20 seconds is travelling at 25.0 m/s. How far will it have travelled during this trip? Show all work as demonstrated in the lessons. 12. A cross-country race car driver sets out on a 1.00 hour, 100.0 km race. At the halfway marker (50.0 km), the pit crew radios that the car had averaged a speed of only 80.0 km/h. a) How long did it take the driver to travel the first 50.0 km? Show all work as demonstrated in the lessons. b) How fast must the driver drive over the remaining distance in order to average 100.0 km/h for the entire race? Show all work as demonstrated in the lessons. 13. A car starts at rest and is moving at a velocity of 25.0 m/s after 18.0 seconds. How far will it have traveled? Show all work as demonstrated in the lessons. 14. A cat's displacement is 15 meters to the right in 7.0 seconds. If, at the start of the 7.0 seconds, the cat was moving at a velocity of 2.0 m/s left what was its final velocity? Show all work as demonstrated in the lessons.6. A satellite in space is travelling at 14 m/s in one direction. A thruster is applied for 30. s and the satellite is then travelling at 12 m/s in the opposite direction. What acceleration does the thrust cause? Show all work as demonstrated in the lessons. 7. A rock is dropped off a 40. meter cliff. The rock accelerates due to gravity. What is the time it takes to hit the ground? Show all work as demonstrated in the lessons. 8. A motorcycle is travelling at a constant velocity of 90 km/h (no acceleration). How many seconds will it take the motorcycle to cover 2 km? Show all work as demonstrated in the lessons. 9. Hikers at the bottom of a canyon are facing towards the canyon wall 280.5 meters away. Given that the speed of sound in air is 340. m/s, how long after they shout will they hear their echo? Show all work as demonstrated in the lessons. 10. A woman makes a daytrip to a beach that is located 40.0 km from her home. On the trip to the beach, she averages a speed of 80.0 km/h but gets a speeding ticket upon her arrival. On the return trip, she averages just 40.0 km/h. What was her average speed for the entire trip? Show all work as demonstrated in the lessons.11. Provide a description of a sample situation for each of the graphs below (make sure to recognize each graph as d vs t, v vs t, or a vs t). d TTTTTT2. Determine the slope of the graph (show all work and include units) at the different portions of the flight. a. Determine an approximate slope in the t = 3-9 second range (show all work): b. Determine an approximate slope in the t = 12-16 second range (show all work): 0. Determine an approximate slope in the t = 19-24 second range (show all work): d. What do you think the slope represents? Try to explain how this makes sense in the ranges above. No \"wrong answers" answers here as long as some thought is shown. 3. Graph the same data using a spreadsheet. Include a printout of both the table and the graph along with your Learning Guide when you submit. Graphing MOTION: 1. Define slope, and then sketch some example slopes (positive, negative, zero, and undefined). 2. The slope of a d vs t graph represents . Describe 3 ways you know this to be true. 3. The motion of two runners is graphed below (Alasie and Brent). A a) Do they start at the same point? How do E 3-; you know? b) At 2 seconds, who is ahead? (J'I 444444444444 rig) c) At 8 seconds, who is ahead? d) Which is running faster? How do you know? e) What is happening at t= 5 seconds? 14. A rock is thrown downwards with an initial velocity of 8.0 mfs. What is the velocity of the rock after 1.5 s? 15. The direction of acceleration is determined by the change in velocity (Av = Vf v0). Complete the following table, then below the table invent a situation where these velocities might happen. \"A\" is done for you. a [pas or neg) A. A person. at a stopL'Lgl/itpmsses the gas aw! goes from still (0W5) to loud/S 16. Explain why the following misconceptions are false. a) If acceleration is zero, the object must be standing still. b) Velocity and acceleration are always the same sign (both positive or both negative). c) If speed is increasing, acceleration must be positive. 15. A bus traveling at 80.0 km/h accelerates for 12 s to a speed of 100. km/h. What was the acceleration? Show all work as demonstrated in the lessons. 16. A small stone is dropped and spends 6.0 seconds in the air until it strikes the ground. What speed is it moving when it reaches the ground? Show all work as demonstrated in the lessons. 17. A cyclist, starting from rest, achieves a speed of 15 m/s after traveling 22.5 m. What was the acceleration? Show all work as demonstrated in the lessons. 18. A child on a toboggan slides down a snowy hill, accelerating uniformly at 2.8 m/s2. When the toboggan passes the first observer, it is travelling with a speed of 1.4 m/s. How fast will it be moving when it passes a second observer, who is 2.5 m downhill from the first observer? Show all work as demonstrated in the lessons. 19. A formula 1 race car travelling at 100. m/s can decelerate at 20. m/s2. How far in advance must the brakes be applied to come to a stop?6. Can three vectors of different magnitudes and directions add to zero? Show with a vector diagram below. 17. As difficult as it is to visualize the changes in velocity, a good understanding of acceleration is needed to master kinematics problems. Recognizing that acceleration can be positive, while velocity is negative (and vice versa) can be challenging. a. Object is speeding up (from still) in the positive direction. For example, a ball is placed on a slanted ramp. Velocity is positive / zero / negative and increasing / constant /decreasing. Acceleration is positive / zero / negative. b. Object is speeding up (from still) in the negative direction. For example, a ball is placed on a ramp that is slanted towards the negative direction (eg. down to the left). Velocity is positive / zero / negative and increasing / constant /decreasing. Acceleration is positive / zero / negative. c. Object is slowing down in the positive direction. For example, you push a ball up a slanted ramp. Velocity is positive / zero / negative and increasing / constant /decreasing. Acceleration is positive / zero / negative. d. Object is slowing down in the negative direction. For example, you push a ball up a ramp that is slanted towards the negative direction (eg. down to the right). Velocity is positive / zero / negative and increasing / constant /decreasing. Acceleration is positive / zero / negative. 18. Review your results from the previous question to build general statements that are always true: Acceleration is always in the opposite direction of if the object is slowing down. Acceleration is always in the same direction of if the object is speeding up.8. The motion of a race car on a linear track is shown below. velocity a) When is the car at the (m/min) starting line? 80 60 40 b) When is the car sitting still? 20 time min) . 20 C) When is the car going in the negative direction? - 40 10 20 30 40 50 d) What is the fastest speed logged? Show all work. e) What is the average acceleration of the car between 0 and 10 minutes? Show all work. 9. Use both area and equation to determine the displacement traveled in the following graph. 3 +101 Velocity (m/s) 0 2 3 4 Time (s) -101 10. Use both area and equation to determine the displacement traveled in the following graph. 16 12 Velocity (m/s) -+ 00 3 4 5 Time (s)1. List all the motion/kinematic equations on your formula sheet. NotVe V It, art, devot + zat, Uf = Votat 2 2. List EVERY variable used in the above equations telling what each represents, along with common units for each. Vo =initial velocity d=distance, displacement Vf = final velocity a = acceleration titime 3. What's the difference between average velocity and instantaneous velocity? 4. A canoe travels 320 m east in a time of 120 s. What is the canoe's average velocity? Show the equation used and all steps. 5. A person, originally at the starting line, runs west at 6.5 m/s. What is the runner's displacement after 14s? Show the equation used and all steps.1. Refer to the \"Plotting Data\" lesson (end of "Patterns to Notice") and plot the "Skydiver Velocity vs. Time\" data (taken from the video) on the following graph. to c) d) e) f) 9) Which is the independent variable? Which is the dependent variable? _ Title and units for the xaxis = . . (make sure included on graph) Title and units for the y-axis = ' ' (make sure included on graph) Overall title of graph = ' (make sure included on graph) Connect the points in each distinct region with a series of "best t lines\" to represent your data. 1. The pool ball shown below was photographed 8 times at equal time intervals. Is the pool ball's motion uniform? How do you know? Sketch a d vs t and v vs t graph, showing the general shape of each graph. 2. Make a sketch of what the pool ball's photos would look like if it were accelerating (both positively and negatively). 3. Acceleration is often a difficult term to understand. How could you best explain the acceleration of a car (and how it's different then velocity) to a non-physicist? 4. How can you recognize uniform motion on a d vs t graph? 5. What are common units for the following: a. Displacement / Distance (provide 6 examples and circle the SI standard one): b. Time (provide 3 and circle the SI standard one): c. Velocity / Speed (provide 4 and circle the SI standard one): d. Acceleration (provide 3 and circle the SI standard one):6. Below is a graph of a ball's motion. Provide an interpretation of the ball's motion. A Position (m) N 5 Time (s) 7. A man starts at the starting line, walks back slowly and steadily for 6 seconds. Then he stands still for 6 seconds, then walks forward steadily about twice as fast for 6 seconds. Sketch the d vs t and v vs t graphs showing this motion. 8. A car is traveling down the road. Its v vs. t graph is shown below. Sketch the d vs t graph that shows the motion. Velocity (m/s) Time ( s ) 9. A car is moving forward when the brakes are applied. Sketch the d vs t graph of this motion. Show some tangent lines on your graph showing fast, slower, stopped