Equations of Motion Quiz
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Questions and Answers

What is the initial velocity (v0) of the pebble at the moment it is dropped?

  • 3.0 m/s
  • 0.0 m/s (correct)
  • 9.8 m/s
  • 5.0 m/s
  • The acceleration of the pebble is positive as it falls down.

    False

    What is the displacement of the pebble after three seconds?

    -44.1 m

    All objects in free fall descend under the constant acceleration of ________.

    <p>9.8 m/s²</p> Signup and view all the answers

    Match the following terms with their definitions:

    <p>Displacement = The change in position of an object Velocity = The speed of an object in a given direction Acceleration = The rate of change of velocity Force = A push or pull on an object</p> Signup and view all the answers

    What does acceleration represent in physics?

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

    The displacement of an object is calculated as the final position minus the initial position.

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

    What is the formula to calculate average acceleration?

    <p>a = (v - v0) / Δt</p> Signup and view all the answers

    What does the displacement equation represent when a car travels at a constant velocity?

    <p>The initial position plus velocity times time</p> Signup and view all the answers

    Acceleration can be defined as the change in _____________ of an object in a given time interval.

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

    If a car experiences constant acceleration, the displacement is given by $x - x_0 = v_0 t + at^2$.

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

    If a car has an initial velocity of +10 m/s and a constant acceleration of 2 m/s², what will its final velocity be after 5 seconds?

    <p>+30 m/s</p> Signup and view all the answers

    What happens to the displacement equation when the initial position is zero?

    <p>The first term disappears.</p> Signup and view all the answers

    Displacement is defined as the __________ position minus the __________ position.

    <p>final, initial</p> Signup and view all the answers

    Displacement can also be calculated using the equation $x = x_0 + v_0 t + _____$.

    <p>at^2/2</p> Signup and view all the answers

    What is the final velocity of an object under constant acceleration after a certain time if its initial velocity is 15 m/s and it accelerates at 3 m/s² for 4 seconds?

    <p>27 m/s</p> Signup and view all the answers

    In a scenario where initial velocity and initial position are both zero, what does the displacement equation simplify to?

    <p>x = at^2</p> Signup and view all the answers

    Match the following variables with their meanings:

    <p>v = Final velocity v0 = Initial velocity a = Acceleration t = Time</p> Signup and view all the answers

    What is the term that represents constant change in velocity?

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

    If a box has an initial velocity of +10 m/s and a constant acceleration of -1 m/s^2, its displacement after 10 seconds will be given by: $x = v_0 t + _____$.

    <p>-0.5at^2</p> Signup and view all the answers

    Match the following terms to their definitions:

    <p>Displacement = The change in position of an object Velocity = The speed of an object in a specific direction Acceleration = The rate of change of velocity Time = The duration a motion occurs</p> Signup and view all the answers

    What is the simplified displacement equation when the initial position is set to zero?

    <p>x = v0t + at</p> Signup and view all the answers

    The alternate velocity equation v2 = v0^2 + 2ax can be used for three-dimensional motion.

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

    What is the total displacement of the box from its initial position after 10 seconds if the displacement calculation is 100 m + 1(-100 m)?

    <p>50 m</p> Signup and view all the answers

    The general displacement equation is given by x = x0 + v0t + ___t^2.

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

    If an airplane has an initial speed of +15 m/s and accelerates at +6 m/s² over 600 m, what is its final velocity?

    <p>70 m/s</p> Signup and view all the answers

    In the equation v = v0 + at, a represents the ___ of the object.

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

    Match the term with its definition:

    <p>x = Displacement of an object v0 = Initial velocity a = Acceleration t = Time</p> Signup and view all the answers

    What is the significance of setting the initial velocity (v0) to zero in the equation v2 = v0^2 + 2ax?

    <p>It simplifies the equation to v2 = 2ax.</p> Signup and view all the answers

    Study Notes

    Equations of Motion

    • Objective: Solve problems for objects with constant acceleration, linking displacement, velocity, acceleration, and time.

    Key Kinematic Equations

    • Acceleration (a) is the change in velocity (v) over time (t): ( a = \frac{\Delta v}{\Delta t} = \frac{v - v_0}{t} ).
    • Final velocity (v) can be calculated as: ( v = v_0 + at ), where:
      • ( v_0 ): initial velocity (m/s)
      • ( a ): acceleration (m/s²)
      • ( t ): time (s)

    Example of Constant Acceleration

    • If a car has an initial velocity of +10 m/s and accelerates at 2 m/s² over 5 seconds, final velocity can be calculated as:
      • ( v = +10 , \text{m/s} + (2 , \text{m/s}²)(5 , \text{s}) = +20 , \text{m/s} ).

    Displacement and Its Equation

    • Displacement (( \Delta x )) is the change in position: ( \Delta x = x - x_0 ).
    • For constant velocity ( v_0 ): ( \Delta x = v_0 t ).
    • With constant acceleration (( a )), the displacement equation becomes:
      • ( \Delta x = v_0 t + \frac{1}{2} a t^2 ).
    • Rearranged to solve for final position:
      • ( x = x_0 + v_0 t + \frac{1}{2} a t^2 ).

    Practical Example of Displacement

    • A box on a conveyor with initial velocity of +10 m/s and acceleration of -1 m/s²:
      • Over 10 seconds, total displacement is calculated using:
      • ( x = 0 + (+10)(10) + \frac{1}{2}(-1)(10^2) = 100 - 50 = 50 ) meters.

    Alternate Velocity Equation

    • Alternate equation for one-dimensional motion with acceleration:
      • ( v^2 = v_0^2 + 2ax ).
    • This allows calculation of any variable (v, ( v_0 ), ( a ), or ( x )) if acceleration and other parameters are known.
    • Simplifies to ( v^2 = 2ax ) when ( v_0 = 0 ).

    Example of Finding Velocity

    • If an airplane starts at +15 m/s, accelerates at +6 m/s² over 600 meters:
      • Use: ( v^2 = (15 , \text{m/s})^2 + 2(6 , \text{m/s}²)(600 , \text{m}) ) to find final velocity.

    Projectile Motion

    • For objects in free fall, such as a pebble dropped from a height:
      • Values are: ( v_0 = 0 , \text{m/s} ), ( a = -9.8 , \text{m/s}² ) (due to gravity), ( t = 3.0 , \text{s} ).
    • Displacement (( y )) after 3 seconds is calculated as:
      • ( y = v_0 t + \frac{1}{2} a t^2 ).

    Free Fall Characteristics

    • Constant acceleration due to gravity (approximately -9.8 m/s²).
    • Free fall continues unless acted upon by external forces, like air resistance, which can lead to terminal velocity—the maximum velocity where forces balance.

    Summary

    • Objects in free fall experience constant acceleration due to gravity, unaffected unless external forces apply. Air resistance can ultimately oppose gravity and stabilize at terminal velocity.

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    Related Documents

    Equations of Motion PDF

    Description

    Test your understanding of the equations of motion and kinematics in this quiz. You'll solve problems involving displacement, velocity, acceleration, and time for objects moving with constant acceleration. Be prepared to apply the formulas and concepts learned in this lesson.

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