(II) Figure 2–42 shows the velocity of a train as a function of time. When was the magnitude of the acceleration greatest?
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2. 1D Motion / Kinematics
Velocity-Time Graphs & Acceleration
Problem 13
Textbook Question
The table shows test data for the Bugatti Veyron Super Sport, the fastest street car made. The car is moving in a straight line (the -axis).
(a) Sketch a - graph of this car's velocity (in mi/h) as a function of time. Is its acceleration constant?
(b) Calculate the car's average acceleration (in m/s2) between (i) and s; (ii) s and s; (iii) s and s. Are these results consistent with your graph in part (a)? (Before you decide to buy this car, it might be helpful to know that only will be built, it runs out of gas in minutes at top speed, and it costs more than million!)


1
Step 1: To sketch the v_x-t graph, plot the given data points on a graph with time (t) on the x-axis and velocity (v_x) on the y-axis. Connect the points to visualize the velocity changes over time.
Step 2: Analyze the graph to determine if the acceleration is constant. Constant acceleration would be indicated by a straight line on the v_x-t graph. If the line is not straight, the acceleration is not constant.
Step 3: To calculate the average acceleration between 0 and 2.1 s, use the formula: a_avg = (v_f - v_i) / (t_f - t_i), where v_f and v_i are the final and initial velocities, and t_f and t_i are the final and initial times. Convert velocities from mi/h to m/s by multiplying by 0.44704.
Step 4: Repeat the average acceleration calculation for the intervals 2.1 s to 20.0 s and 20.0 s to 53 s using the same formula. Ensure to convert all velocities to m/s before calculating.
Step 5: Compare the calculated average accelerations with the graph from part (a) to check for consistency. If the graph shows varying slopes, the accelerations should differ, indicating non-constant acceleration.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Velocity-Time Graph
A velocity-time (v-t) graph represents how an object's velocity changes over time. The slope of the graph indicates the object's acceleration. A straight line suggests constant acceleration, while a curve indicates changing acceleration. In this problem, sketching the v-t graph helps visualize the car's velocity changes and assess whether its acceleration is constant.
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Velocity-Time Graphs & Acceleration
Average Acceleration
Average acceleration is defined as the change in velocity divided by the time over which the change occurs. It is calculated using the formula a_avg = (v_f - v_i) / (t_f - t_i), where v_f and v_i are the final and initial velocities, and t_f and t_i are the final and initial times. This concept is crucial for determining the car's acceleration over specified time intervals.
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Solving Constant and Average Velocity Problems
Unit Conversion
Unit conversion is essential when working with different measurement systems. In this problem, velocities are given in miles per hour (mi/h), but acceleration needs to be calculated in meters per second squared (m/s²). Converting units accurately ensures correct calculations and comparisons, such as using 1 mi/h = 0.44704 m/s for velocity conversion.
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Unit Conversions
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