a) Use the graph above and calculate the slope of the line for each case. Explain how you calculated the slope. How is the slope similar to the index?

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1 Slopes and Expressions: Speed and Velocity 5.1 Observe and Represent Another way of comparing trend lines is by calculating the slope of each line and comparing the numerical values of the slopes. a) Use the graph above and calculate the slope of the line for each case. Explain how you calculated the slope. How is the slope similar to the index? Need Some Help? Slope: is often used to describe the measurement of the steepness of a straight line. A higher slope value indicates a steeper incline. The slope is defined as the ratio of the change in the value of the dependent variable (vertical axis) over the change in the value of the independent variable (horizontal axis). In other words, vertical change divided by horizontal change! b) For the skiers, what do you think the slope of the line represents? c) What are the units of this slope? How do you know? d) Write an expression that will allow you to find each skier s position (x) for any time (t).

2 5.2 Test Your Idea If these expressions that you have been writing really do represent motion accurately, it should be possible to use them to predict position of a moving object if we know the type of motion that occurs. To do so we will use the PhET simulation, The Moving Man. You should navigate to the following web address and click, Run Now. a. Sketch, draw a dot diagram, and write an expression for the man walking at a speed of 0.3 m/s who starts moving from position zero when we start our observations. b. Use this expression to predict where the man will be after 8 seconds. c. In the Moving Man simulation, type 0.3 in the velocity box. Make sure that the man begin at position zero and zero clock reading. d. Then click Go. Just before the man gets to the wall click, Stop. This can be located at the bottom of the simulation. e. Move the gray bar on the graph to 8 seconds to check your mathematical prediction of the position. f. Did your prediction match the actual outcome? Make sure to check you work and discuss any problems you may have had.

3 Did You Know? Velocity and speed for constant speed linear motion: Velocity is the slope of the position versus time graph. The unit of velocity is m/s, miles/h, km/h, and so forth. Positive velocity means that the object is moving in the positive direction, negative means in the negative direction. Speed is velocity without specifying direction; therefore it is always positive. For constant speed, velocity can be written as: x! = vt + x! x 2 x 1 = ( x) = change in position t 2 t 1 = ( t) = time interval 5.3 Problem Solving Practice Answer each of the following questions. Remember to circle, box, and underline the important information in the word problem. Include a sketch and a dot diagram with each answer. a) A bullet is fired with a speed of 720 m/s. What time is required for the bullet to strike a target at a position 324 m? b) A turtle crawls at 10 cm/s. How long will it take the turtle to go 2 m?

4 c) Sound travels at 330 m/s. You see an explosion and notice that it takes 4.5 s for the sound to reach you. How far away was the explosion? d) How long will it take a plane to fly from NY to LA (2950 miles) if the plane travels at 450 miles/hour? e) The slowest animal ever discovered was a crab found in the Red Sea. It traveled with an average speed of 5.70 km/year. How long will it take for this crab to travel 100 km?

5 f) A car drives 180 km in 3 hours. How fast is it traveling? g) A jogger travels 5 m/s and goes meters. How long (time) did she travel? h) A jogger runs 100 m at a constant speed of 5 m/s and then, becoming tired, walks 100 m at a constant speed of 1 m/s. How long does the jogger work out?

6 i) A man traveling 100 meters/minute walks for 3 hours. How far has he traveled? Unit conversion required. j) A good runner can do the 100-meter dash in 11 seconds. How fast is this in m/s and km/hr? Unit conversion required.