Physics Chapter 3: Vector Form of Acceleration
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Questions and Answers

What were the subcategories that Sir Isaac Newton broke down his subject into?

  • Motion, forces, and other phenomena (correct)
  • Gravity, electricity, and magnetism
  • Acceleration, velocity, and speed
  • Energy, momentum, and velocity

    • In what manner did Sir Isaac Newton work out the first basic task?

  • Intuitively and descriptively, with a bias toward vagueness
  • Empirically and numerically, with a bias toward uncertainty
  • Conceptually and mathematically, with a bias toward simplicity (correct)
  • Experimentally and theoretically, with a bias toward complexity

    • How would you describe the directions used on a piece of graph paper to represent a route?

  • Parallel directions a and b
  • Vertical and horizontal directions
  • Perpendicular directions x and y (correct)
  • Diagonal and slanting directions

    • What information would you provide to indicate your position using a pair of numbers?

    <p>Measurable distances after each turn</p> Signup and view all the answers

    What is the instantaneous speed?

    <p>The exact speed at a specific instant of time</p> Signup and view all the answers

    What is the informal speedometer speed close to?

    <p>Average speed over a finite, short time interval</p> Signup and view all the answers

    What does the graph of speed versus time represent?

    <p>Distance travelled</p> Signup and view all the answers

    How does one calculate the distance for something that is not traveling at constant speed?

    <p>Using the distance rectangle formula</p> Signup and view all the answers

    What quantity measures the change of velocity in an acceleration?

    <p>Acceleration</p> Signup and view all the answers

    What is used to denote average speed in physics terms?

    <p>$ar{v}$</p> Signup and view all the answers

    What measures the rate of change of velocity over time?

    <p>$a$</p> Signup and view all the answers

    What does instantaneous speed purport to describe?

    <p>Average speed for an infinitesimally small time interval</p> Signup and view all the answers

    What does the author want to make descriptions and predictions for?

    <p>The position of a baseball</p> Signup and view all the answers

    What do the nature of the predictions depend on?

    <p>The interaction between a baseball and the gravitational field of Earth</p> Signup and view all the answers

    What concept does the author want to apply in making predictions about the baseball and proton?

    <p>Professor Galileo's concept of states of motion</p> Signup and view all the answers

    Where is the Large Hadron Collider located?

    <p>Geneva, Switzerland</p> Signup and view all the answers

    What does a velocity measure in addition to direction?

    <p>Speed</p> Signup and view all the answers

    When working out a complex set of directions, what mathematical concept is required?

    <p>Trigonometry</p> Signup and view all the answers

    What is the customary speed rating system in the United States?

    <p>mph</p> Signup and view all the answers

    What does the speed formula calculate?

    <p>Speed at any specific instant of time</p> Signup and view all the answers

    How does taking a 30-minute nap and donuts break affect speed calculation?

    <p>Does not affect speed calculation</p> Signup and view all the answers

    What does the average speed formula add up and then divide by?

    <p>Number of measurements</p> Signup and view all the answers

    Which mathematical concept is used to calculate the exact direction of travel?

    <p>Trigonometry</p> Signup and view all the answers

    What does mph stand for?

    <p>Miles per hour</p> Signup and view all the answers

    What does the numerator of the speed formula represent?

    <p>Distance interval</p> Signup and view all the answers

    What does instantaneous speed refer to?

    <p>Average speed at any specific instant of time</p> Signup and view all the answers

    What does the denominator in the formula for speed represent?

    <p>Elapsed time</p> Signup and view all the answers

    What does an average speed provide an imperfect, approximate description of?

    <p>The distance traveled over a long time interval</p> Signup and view all the answers

    What is the traditional starting point in a spatial location system?

    <p>(0, 0, 0)</p> Signup and view all the answers

    What was the initial material used to create a meter?

    <p>Platinum and iridium metals</p> Signup and view all the answers

    What was the measure of a meter set to be initially?

    <p>One ten-millionth of the distance from the Equator to the North Pole</p> Signup and view all the answers

    What does (2, 3, 3) refer to in terms of spatial location?

    <p>2 blocks east, 3 blocks north, and 3rd floor</p> Signup and view all the answers

    What does the meter initially represent?

    <p>A fraction of a line of longitude from the Equator to the North Pole</p> Signup and view all the answers

    How was a solar day defined by the Egyptians?

    <p>Divided into twelve hours of daylight and twelve hours of darkness</p> Signup and view all the answers

    What is the measure of an hour in modern solar time?

    <p>60 minutes</p> Signup and view all the answers

    What is an hour divided into according to Sumerian style?

    <p>60 equal parts</p> Signup and view all the answers

    Which year marked the final refinement to define a meter based on the speed of light?

    <p>1983</p> Signup and view all the answers

    What event does high noon mark?

    <p>The time when the sun is due south on a given day</p> Signup and view all the answers

    What is the frequency of the microwave radiation emitted by cesium atoms in the cesium atomic clock?

    <p>9.192631770 GHz</p> Signup and view all the answers

    How is one gram defined?

    <p>The mass of a cubic centimeter of liquid water at 0°C</p> Signup and view all the answers

    What is a kilogram based on?

    <p>The mass of a liter of water</p> Signup and view all the answers

    What is the difference between mass and weight?

    <p>Weight changes on the moon, mass remains the same</p> Signup and view all the answers

    How can you distinguish between velocity and speed in physics?

    <p>Velocity includes direction, speed does not</p> Signup and view all the answers

    What is the purpose of a balance in measuring an unknown mass?

    <p>To measure the mass of an object</p> Signup and view all the answers

    How do initial conditions change over time?

    <p>They change according to accelerations</p> Signup and view all the answers

    What does velocity in physics indicate?

    <p>It measures both speed and direction</p> Signup and view all the answers

    What does a kilogram measure?

    <p>The amount of matter in an object</p> Signup and view all the answers

    What is the purpose of using liters of water while measuring an unknown mass?

    <p>To balance out the unknown mass with a known volume</p> Signup and view all the answers

    What does taking an object to the moon illustrate about its mass and weight?

    <p>It illustrates that weight changes but mass remains constant on the moon.</p> Signup and view all the answers

    What does the frequency emitted by cesium atoms in the cesium atomic clock enable us to measure?

    <p>Time duration accurately.</p> Signup and view all the answers

    What does a negative acceleration signify?

    <p>The speed is decreasing over time.</p> Signup and view all the answers

    What does the area under the velocity graph represent when an object is slowing down?

    <p>The stopping distance.</p> Signup and view all the answers

    What is the acceleration experienced by the accelerating Shelby in terms of meters per second squared?

    <p>7.66 m/s^2</p> Signup and view all the answers

    What does the smooth triangle on the velocity graph represent?

    <p>Distance traveled using instantaneous speeds.</p> Signup and view all the answers

    What does the change of speed ($ riangle v$) formula allow you to calculate?

    <p>Change in speed over time</p> Signup and view all the answers

    In the context of motion, what does 'cross multiplication' allow you to do?

    <p>Calculate the change in speed under known acceleration.</p> Signup and view all the answers

    What does a negative slope on the velocity graph indicate?

    <p>The object is slowing down.</p> Signup and view all the answers

    What does the area of the yellow triangle express?

    <p>The distance travelled</p> Signup and view all the answers

    In what context would you use the distance triangle formula?

    <p>For calculating distance traveled from rest</p> Signup and view all the answers

    What does a smooth triangle on a velocity graph indicate?

    <p>Instantaneous speed</p> Signup and view all the answers

    What is the purpose of the distance calculations mentioned in the text?

    <p>To predict the position of a baseball or velocity of a proton</p> Signup and view all the answers

    What concept do the distance calculations help apply?

    <p>Galileo's laws of motion</p> Signup and view all the answers

    What type of interactions are involved in the predictions mentioned in the text?

    <p>Baseball interacting with the gravitational field and proton interacting with the magnetic field</p> Signup and view all the answers

    What is the essential nature of the predictions based on the text?

    <p>Dependent on different interactions and fields</p> Signup and view all the answers

    What does Sir Isaac Newton's instruction, "...from the phaenomena of motions to investigate the forces of nature..." imply?

    <p>To understand forces through observations of motion</p> Signup and view all the answers

    Which breakthrough ideas concerning states of motion are mentioned in the text?

    <p>Galileo's laws of motion</p> Signup and view all the answers

    What was Sir Isaac Newton's instruction, as mentioned in the text, for understanding the forces of nature?

    <p>&quot;...from the phaenomena of motions to investigate the forces of nature...&quot;</p> Signup and view all the answers

    Study Notes

    Acceleration and Velocity

    • Acceleration is defined in vector form and applies to motion in three dimensions.
    • A change in the direction of the velocity vector constitutes acceleration.
    • Acceleration can be calculated through the formula for change of speed, allowing calculation under constant acceleration over time.

    Shelby Performance Example

    • The Shelby achieves an acceleration of 7.66 m/s², increasing speed for each second of acceleration.
    • After 2 seconds, the speed recorded would be 15.32 m/s.
    • Calculating distance involves average speeds over time intervals, which can be represented on a speed versus time graph resembling a triangle.

    Distance Calculation Methods

    • Using half-second intervals gives a more accurate representation but still relies on average speeds for area under the curve approximation.
    • Instantaneous speed provides an exact calculation with infinitesimal time intervals, allowing for precise distance calculations as areas of shapes like triangles.

    Slowing Down and Stopping Distance

    • Negative acceleration indicates slowing down, resulting in a negative slope on the velocity graph, which still contributes to the total stopping distance.
    • The concept of motion is explored through Newton’s framework, which emphasizes understanding motion categories and their mathematical representation.

    Measuring Position in Three-Dimensional Space

    • Position can be described with three coordinates (x, y, z) relative to a defined origin.
    • Clear identification of measurement systems is essential, as units can vary (meters, miles, etc.).

    Definition of a Meter

    • A meter is defined as one ten-millionth of the distance from the Equator to the North Pole.
    • The standard measurement has evolved to define a meter based on the distance light travels in a specific fraction of a second.

    Definition of a Second

    • The second initially derived from Earth's rotation, divided by 60, is now defined by the frequency of microwave radiation emitted by cesium atoms.

    Definition of a Kilogram

    • One kilogram is the mass of one liter of water, anchored in metric measurements.
    • Balances are traditionally used to determine mass based on the weight of water.

    Distinguishing Mass from Weight

    • Mass remains constant regardless of location; weight varies with gravity, showcasing the difference when comparing Earth and the Moon.

    Predicting Position Over Time

    • Accurate predictions of an object's position depend on its initial conditions and acceleration, necessary for modeling object movement over time.

    Understanding Velocity

    • Velocity comprises both speed and direction, represented mathematically as a vector.
    • Speed is quantified in different units (e.g., m/s, mph) and is essential for determining travel time and distance.

    Calculating Direction and Speed

    • Direction can be expressed trigonometric terms or simpler ordinal directions (e.g., north, southwest).
    • Speeds can be calculated by dividing distance by time, allowing for changes in measurement units (e.g., from miles to meters).

    Average Speed vs. Instantaneous Speed

    • Average speed is calculated over time intervals yet may not accurately reflect instantaneous changes during travel.
    • Instantaneous speed is represented by speedometer readings, which provide valuable real-time data despite representing average lapses.### Instantaneous Speed vs. Average Speed
    • Instantaneous speed measures exact speed at a specific moment; akin to average speed over an infinitesimally small interval.
    • Speedometer readings represent a short-term average speed, close to instantaneous speed but for a finite time interval.

    The Tortoise and the Hare Fable

    • The hare has significantly higher instantaneous speeds than the tortoise.
    • The hare's naps reduce his average speed, allowing the tortoise, which maintains a steady pace, to win.
    • Tortoise starts at 0 ft/min, reaches 100 ft/min after one minute, giving him an average speed of 50 ft/min for that minute.
    • The tortoise maintains a speed of 100 ft/min for the remainder of his 30-minute journey to Dunkin Donuts.
    • The hare's initial minute averages 860 ft/min, covering 860 feet, but his speed fluctuates:
      • Second minute: average speed 464 ft/min, total distance 1324 feet.
      • Fifth minute: speed drops to 257 ft/min, total distance 2741 feet.
    • While the hare naps, the tortoise progresses and ultimately reaches 2950 feet, winning the race.

    Speed Graph Interpretation

    • In graphs of speed versus time, the distance traveled (Δx) during an interval equals the area of a rectangle formed by average speed and the width of the time interval.
    • Rectangle's height represents average speed; this area gives distance at constant speed.

    Acceleration Concept

    • Acceleration refers to the change in speed of an object, either increasing or decreasing.
    • Formula for acceleration includes both change in speed and the time taken to achieve that change.
    • Example: A Shelby Cobra accelerates from 0 to 60 mph in slightly over 3 seconds, while a slower vehicle, such as a Ford Pinto, takes significantly longer.
    • In acceleration formulas, the time taken influences the acceleration rate; greater time results in smaller acceleration.

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    Description

    Test your understanding of the vector form of acceleration and velocity, and their application to motion in three dimensions. Explore the calculation of speed change under known acceleration during a specific elapsed time.

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