a) An object decreasing speed then increasing speed in the opposite direction.

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1 Putting it all Together 10.1 Practice Use the kinematics equations to solve the following problems: a) You throw a marble up at the speed of 10 m/s. What is its maximum height? b) You drop a marble from a height of 1.5 m. What is the speed t which it will reach just before it hits the ground? c) A bus slows down from 15 m/s to 10 m/s in 200 meters. What is the acceleration of the bus? d) A bullet traveling at a speed of 200m/s passed through a wooden block and gets stuck in it right as it is ready to come out. What is the acceleration of the bullet if the block is 40 cm wide? (pay attention to units here) 10.2 Represent and Reason Fill in the missing information on the graphs below. Match the description with the vertical set of graphs. a) An object decreasing speed then increasing speed in the opposite direction. b) An object increasing speed c) An object traveling at a constant velocity

2 10.3 Represent and Reason Fill in the missing information on the graphs below. For each set of vertical graphs, describe the motion for each segment. (m/ (m/

3 10.4 Regular problem A shuttle bus slows to a stop to avoid hitting a deer that had darted into the middle of the road. If the bus was initially traveling at m/s and had an average acceleration of m/s/s, what distance would it need to travel to avoid the collision? 10.5 Evaluate the Solution Identify any errors in the proposed solution to the following problem and provide a corrected solution if there are errors. The problem: A fire fighter slides down a fire pole at an increasing speed for 2.0 s, a distance of 2.0 m (she holds on so she doesn t move too fast at the bottom). She bends her knees at the bottom and stops in 0.10 m. a) Determine her speed at the end of the slide and just before she contacts the floor. b) What is her acceleration while stopping? Proposed solution: v = v0 + at = 0 + (9.8 m/s 2 )(2.0 s) = 19.6 m/s. a = (v 2 v0 2 ) /2(x x0) = [0 2 (19.6 m/s) 2 ]/2(0.10 m) = m/s Regular Problem A beach ball is volleyed up from a height 2.1m above the ground into up to a height of 13m. Find out the as many unknown physical variables about the initial conditions and 2.5 seconds later Regular Problem Heather and Komila are exercising in the park. When you start observing them, Komila is 50 m ahead of Heather. She is jogging at a speed of 5 mph and Heather is running at the speed of 7 mph. How long will take Heather to catch up with Komila? What assumptions did you make? 10.8 Regular Problem This time Heather and Komila are running towards each other. How long will it take them to meet? What assumptions did you make? 10.9 Regular Problem While concentrating on catching the football, a wide receiver on a football team runs into the goal post. He was originally moving at 10 m/s and bounced back at 2.0 m/s. A video of the collision indicates that it lasted s. Determine the acceleration of the receiver during the collision. Indicate any assumptions you made. How will you model the receiver to solve the problem?

4 10.10 Regular Problem While traveling in your car at 24 m/s, you find that traffic has stopped 30 m in front of you. Will you smash into the back of the car stopped in front of you? Your reaction time is 0.80 s and the magnitude of your car s acceleration is 8.0 m/s 2 after the brakes have been applied. List all assumptions you make Represent and Reason Assume that the positive direction of the x-axis is to the right. A car is moving according to the equation x = -30 (m) - 10 (m/s) t + 3(m/s 2 ) t 2 a) Describe the motion of the car in words. b) Determine the initial position, initial velocity, and acceleration of the car. Does it speed up or slow down? c) Draw a motion diagram for the car. d) Draw a velocity versus time graph for the car. Write a function v(t) for the graph. e) Sketch the position versus time graph right underneath the velocity versus time graph. What do you expect to see on this graph at the instant when the car stops? How far does it travel before it stops? f) How long does it take for the car to stop? What happens after that if the acceleration does not change? Is it a realistic situation? Compare and Contrast Jim says: We learned so many different words: constant velocity, zero velocity, constant acceleration and zero acceleration. I do not understand the difference between them, all sound like motion to me. Do you feel similar to Jim? If you do, it is normal. To help yourself navigate through the new ideas, work through the following exercises Draw a motion diagram for each scenario to help you construct each situation. a) Describe a situation when an object moves with an acceleration equal to zero and a velocity that is a non-zero negative number. b) Describe a situation when an object moves with an constant positive acceleration and velocity is positive number. c) Describe a situation when an object travels with a constant negative acceleration and an positive velocity. d) Describe a situation when an object travels with a constant negative acceleration and a negative velocity.

5 10.14 Represent and Reason A stoplight turns yellow when you are 20 m from the edge of the intersection. Your car is traveling at 12 m/s; after you hit the brakes, the car's speed decreases at a rate of 6.0 m/s each second. (Ignore the reaction time needed to bring your foot from the floor to the brake pedal.) a) Sketch the situation. Decide where the origin of the coordinate system is and what direction is positive. b) Draw a motion diagram. c) Draw an x(t) graph. d) Draw a v(t) graph. e) Draw a a(t) graph. f) Write an expression for x(t) and v(t). g) Use the expressions above to determine as many unknowns as you can Reason and Represent A remote control car runs down a driveway at an initial speed of 6.0 m/s for 8.0 sec, and then uniformly increases its speed to 9.75 m/s in 5.0 sec. a) Sketch the situation, label all knowns and unknowns. Decide where the origin of the coordinate system is and what direction is positive. b) Draw a motion diagram. c) Draw a v(t) graph. d) Draw an a(t) graph. e) Write an expression for x(t) and v(t). f) Use the expressions above to determine as many unknowns as you can Reason What do we mean when we say motion is relative? Why is a reference frame so important? What are the three components of a reference frame? Include a real world example Reflect (possibly as part of your journal entry for this week?) Imagine you could write a note to your past self about solving problems related to motion. What would you say? Make sure that your instructions are helpful for those who are starting the module.

Lesson 12: Position of an Accelerating Object as a Function of Time

Lesson 12: Position of an Accelerating Object as a Function of Time 12.1 Hypothesize (Derive a Mathematical Model) Recall the initial position and clock reading data from the previous lab. When considering