Displacement and Vectors Quiz
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Displacement and Vectors Quiz

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Questions and Answers

What is a base quantity in physics?

  • A quantity that is always measured in metric units
  • A quantity that has no corresponding unit
  • A quantity that must be defined by a standard (correct)
  • A quantity that is defined in terms of other quantities

    • In which system is mass measured in kilograms?

  • International System (SI) (correct)
  • US Customary System
  • British Imperial System
  • CGS system

    • Which of the following is NOT a base quantity?

  • Length
  • Mass
  • Temperature (correct)
  • Time

    • What are derived units?

    <p>Units defined in terms of base units</p> Signup and view all the answers

    Which length unit is representative of the MKS system?

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

    What does displacement represent?

    <p>Magnitude and direction</p> Signup and view all the answers

    What indicates that two vectors are equal?

    <p>Same magnitude and same direction</p> Signup and view all the answers

    How is the negative of a vector defined?

    <p>As a vector with the same magnitude but opposite direction</p> Signup and view all the answers

    What is a scalar quantity?

    <p>A quantity with magnitude only</p> Signup and view all the answers

    Which method is NOT used for adding vectors?

    <p>Head-to-tail method</p> Signup and view all the answers

    If two vectors are perpendicular, how can they be combined?

    <p>Using the Pythagorean theorem</p> Signup and view all the answers

    What does the arrowhead on a vector signify?

    <p>The direction of the vector</p> Signup and view all the answers

    What is the angle of displacement in the example provided involving the skier?

    <p>63°</p> Signup and view all the answers

    What is the equivalent of 1 kilometer in meters?

    <p>1000 m</p> Signup and view all the answers

    Which of the following represents the unit for electric current?

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

    How many grams are in 1 kilogram?

    <p>1000 grams</p> Signup and view all the answers

    What is the prefix for a unit that is larger by a factor of 1000?

    <p>kilo-</p> Signup and view all the answers

    Which unit is used to measure luminous intensity?

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

    Convert 21.5 inches to meters. What is the final value?

    <p>0.546 m</p> Signup and view all the answers

    What is the equivalent of 1 foot in inches?

    <p>12 inches</p> Signup and view all the answers

    How many seconds are in 1 hour?

    <p>3600 s</p> Signup and view all the answers

    What is the equivalent elevation in feet for 8000 meters?

    <p>26,247 ft</p> Signup and view all the answers

    What is the area in square meters of an apartment that measures 880 square feet?

    <p>82 m²</p> Signup and view all the answers

    If the posted speed limit is 55 miles per hour, what is this speed in meters per second?

    <p>25 m/s</p> Signup and view all the answers

    What is the dimension of the area of a triangle?

    <p>[L²]</p> Signup and view all the answers

    Which of the following represents the dimension of speed?

    <p>[L/T]</p> Signup and view all the answers

    When converting from miles per hour to kilometers per hour, which conversion factor is used?

    <p>1 mile = 1.609 km</p> Signup and view all the answers

    What term is used to describe the process of using dimensions to verify the correctness of a relationship?

    <p>Dimensional analysis</p> Signup and view all the answers

    In dimensional analysis, which base unit represents mass?

    <p>[M]</p> Signup and view all the answers

    What is the equation that relates force, mass, and acceleration?

    <p>Force = Mass * Acceleration</p> Signup and view all the answers

    What is the primary distinction between scalar and vector quantities?

    <p>Scalars have only magnitude; vectors have both magnitude and direction.</p> Signup and view all the answers

    In the equation $v = v0 + ½ at^2$, what does $v0$ represent?

    <p>The initial speed of the object</p> Signup and view all the answers

    Why is the equation $v^2 = v0^2 + 2at^2$ considered incorrect?

    <p>Due to conflicting dimensions when summed.</p> Signup and view all the answers

    What does 'displacement' refer to in physics?

    <p>A change in the position of an object.</p> Signup and view all the answers

    What is an example of a vector quantity?

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

    How do scalar quantities combine in calculations?

    <p>Using ordinary arithmetic operations.</p> Signup and view all the answers

    What is the role of the constant (2π) mentioned in the context of dimensional analysis?

    <p>It is dimensionless and does not affect dimensional analysis.</p> Signup and view all the answers

    Study Notes

    Displacement and Vectors

    • Displacement is a vector quantity, meaning it requires both magnitude (distance) and direction to be fully described.
    • Walking 3 km north and 3 km southeast result in different displacements despite the same magnitude.
    • Vectors are represented by boldface italic letters with an arrow above, e.g., A
    • Vectors with the same direction are parallel.
    • Vectors with the same magnitude and direction are equal, regardless of their position in space.
    • The negative of a vector has the same magnitude but the opposite direction.
    • A = -B or B = -A indicates vectors are antiparallel.
    • Scalar quantities are described by a single number and unit, while vector quantities have both magnitude and direction.

    Adding Vectors

    • Vectors can be added using graphical methods:
      • Tail-to-tip method: Place the tail of the second vector at the tip of the first vector, and the resultant vector is drawn from the tail of the first vector to the tip of the second vector.
      • Parallelogram method: Place the tails of the two vectors at the same point, forming two sides of a parallelogram. The diagonal of the parallelogram represents the resultant vector.

    Example: Skiier Displacement

    • A skier travels 1.00 km north and then 2.00 km east.
    • The resultant displacement can be found using the Pythagorean theorem and trigonometry.

    Standards and Units

    • Measurements are made relative to standards or units.
    • Length, time, and mass are fundamental quantities with corresponding base units:
      • Meter (m) for length
      • Second (s) for time
      • Kilogram (kg) for mass
    • SI (International System of Units) is a widely used system of units.

    Using and Converting Units

    • Quantities involve a numerical value and a unit.
    • Conversion factors are used to express quantities in different units.
    • Examples: Converting inches to centimeters and meters, meters to feet, square feet to square meters, miles per hour to meters per second and kilometers per hour.

    Dimensions and Dimensional Analysis

    • Dimensions refer to the types of base units or base quantities (e.g., length, time, mass).
    • Brackets [ ] are used to denote dimensions.
    • Examples:
      • Area: Dimension [L²], Unit: m²
      • Speed: Dimension [L/T], Unit: m/s
      • Acceleration: Dimension [L/T²], Unit: m/s²
      • Force: Dimension [ML/T²], Unit: kg⋅m/s² (Newton)
    • Dimensional analysis can be used to check if equations are dimensionally correct.
    • Example: v = v₀ + ½ at². The dimensions are inconsistent on both sides, indicating an error in the equation.

    Vectors and Vector Addition

    • Vector quantities have both magnitude and direction.
    • Examples: velocity, force.
    • Combining vectors requires specific operations beyond ordinary arithmetic.
    • Displacement is a change in position and is a vector quantity.

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    Description

    Test your understanding of displacement and vectors in physics. This quiz covers key concepts such as vector magnitude, direction, and methods of vector addition. Perfect for students looking to reinforce their knowledge in this fundamental topic.

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