Sketch a graph of how you would expect an instantaneous acceleration vs. time graph to look for a cart released from rest on an inclined track.  Next to this graph, sketch a new graph of the acceleration vs. time for a cart with a much larger mass.  Explain your reasoning.  Write down the equation(s) that best represent each of these graphs.  If there are constants in your equation, what kinematic quantities do they represent?  How would you determine these constants from your graph?

A soccer ball's motion is captured using a motion detector and displayed on the 15 graph shown. Use the graph to answer the following questions. Right is defined as positive. Answers have a 5% tolerance to allow for estimation. 10 Describe the soccer ball's direction of travel: right time (s) Describe the soccer ball's motion: moving at constant speed v 4 8 12 16 20 24 -5 What is the distance traveled? -10 What is the final speed? m/s -15 What is the magnitude of the acceleration? m/s2 velocity (m/s)

Directions: Select all the correct locations on the table. Brett and Jenny were comparing roller coaster data from around the world. The table below shows the information they gathered. Calculate each roller coaster's rate. Use this information to determine which roller coasters have a proportional relationship and select the corresponding rows on the table. Length of Track (feet) Roller Coaster Time of Ride (minutes:seconds) Boomerang Greased Lightning 963.9 1:03 849.5 0:33 Space Mountain 3281.2 2:05 Rajun' Cajun 1377 1:30 Flight of Icarus 1147.5 1:15

Select the graph that best illustrates the story, The figures are labeled (a), (b), (c), and (d). : "You begin your bike ride by riding down a hill. Then you rideup another hill. Finally, you ride along a level surface before coming to a stop."

X 0 C. Kinematics Graphs: Comparison Practice 5 e. A B 6 1. Two identical objects, A and B, move along straight, parallel, horizontal tracks. The graph above represents the position as a function of time for the two objects. t a. At approximately which time or times, if any, are the objects moving at the same speed? If the objects are never moving with the same speed during the interval shown, indicate this explicitly. Briefly explain your answer. b. (b) Describe what is happening to the positions of objects A and B between 0 seconds and 1 seconds. Describe what is happening to the positions of objects A and B between 4 seconds and 5 seconds. d. Which object, if either, has an acceleration with a greater magnitude during the time interval shown in the graph? If the accelerations have the same magnitude for both objects, indicate this explicitly. In a clear, coherent, paragraph-length response, explain your response to part (d). Be sure to reference and compare the graphed information…

Suppose that a car accelerates at a rate of t^2 m/s^2. At the time t = 0, the car is at the 1 m mark and is travelling at 20 m/s,a). how will you express this information as a differential equation b. where is the car at the time, t = 10 s ?c). what is the order of the derived equation?

Shown below are six POSITION vs. TIME graphs. Let WEST be the positive direction. Identify all the graphs that show an object MOVING WEST THE ENTIRE TIME. Then identify all the graphs that show an object MOVING EAST THE ENTIRE TIME. Finally, identify all the graphs that show an object MOVING AT A CONSTANT VELOCITY THE ENTIRE TIME. POSITION vs. TIME GRAPHS MOVING EAST the whole time MOVING WEST the whole time MOVING AT CONSTANT VELOCITY the whole time

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Figure below is a velocity-versus-time graph for a moving object. The object starts at position x = 0. What is the acceleration at t= 1.0 s, in m/s2? Your answer needs to have 3 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement. time in seconds

* e In figure below, the area under the velocity-versus-time graph and between the vertical axis and time t (vertical dashed line) represents the displacement. As shown, this area consists of a rectangle and a triangle. Slope = a. at (a) Compute their areas. (Use any variable or symbol stated above as necessary.) Arectangle Atriangle (b) Explain how the sum of the two areas compares with the expression on the righthand side of x, = x. + vt +