Ch 02: Kinematics in One Dimension

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 02: Kinematics in One Dimension

Problem 61c

Chapter 2, Problem 61c

Ann and Carol are driving their cars along the same straight road. Carol is located at x = 2.4 mi at t = 0 h and drives at a steady 36 mph. Ann, who is traveling in the same direction, is located at x = 0.0 mi at t = 0.50 h and drives at a steady 50 mph. Draw a position-versus-time graph showing the motion of both Ann and Carol.

Verified step by step guidance

Step 1: Understand the problem. We are tasked with drawing a position-versus-time graph for two cars, Ann and Carol, moving along the same straight road. Carol starts at x = 2.4 mi at t = 0 h and drives at a constant speed of 36 mph. Ann starts at x = 0.0 mi at t = 0.50 h and drives at a constant speed of 50 mph.

Step 2: Write the position equation for Carol. Since Carol starts at x = 2.4 mi and moves at a constant speed of 36 mph, her position as a function of time can be expressed as:

x

_c=2.4+36t, where t is in hours and x_c is in miles.

Step 3: Write the position equation for Ann. Ann starts at x = 0.0 mi but begins her motion at t = 0.50 h. Her position as a function of time can be expressed as:

x

_a=50(t-0.50) for t ≥ 0.50 h. For t < 0.50 h, Ann's position remains at x = 0.0 mi.

Step 4: Determine the range of time values to plot. Since Ann starts moving at t = 0.50 h, and both cars are traveling at constant speeds, choose a reasonable time range (e.g., 0 h to 2 h) to observe their motion and potential intersection point on the graph.

Step 5: Plot the position-versus-time graph. On the graph, the x-axis represents time (t) in hours, and the y-axis represents position (x) in miles. Plot Carol's position using her equation

x

_c=2.4+36t as a straight line starting at x = 2.4 mi at t = 0 h. For Ann, plot her position using her equation

x

_a=50(t-0.50) starting at t = 0.50 h. Ensure the graph shows both lines clearly and their intersection point, if any.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Position vs. Time Graph

A position vs. time graph visually represents the location of an object over time. The x-axis typically represents time, while the y-axis represents position. The slope of the line indicates the object's speed; a steeper slope means a higher speed. This graph is essential for understanding how the positions of Ann and Carol change as they drive.

Constant Velocity

Constant velocity refers to an object moving at a steady speed in a straight line without changing direction. In this scenario, both Ann and Carol maintain constant speeds of 50 mph and 36 mph, respectively. This concept is crucial for determining the linear equations that describe their positions over time, which will be used to plot their paths on the graph.

Relative Position

Relative position is the location of one object in relation to another. In this case, Carol starts at 2.4 miles, while Ann starts at 0.0 miles, but at a later time. Understanding their relative positions at any given time is key to accurately plotting their movements on the graph and analyzing when and where they might meet.

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Intro to Relative Motion (Relative Velocity)

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