Rectilinear Erratic Motion Concepts
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Questions and Answers

What is the initial speed of the boat before it is subjected to acceleration?

  • 0 m/s
  • 8 m/s (correct)
  • 10 m/s
  • 4 m/s

    • From what state does the rocket begin its motion?

  • At a speed of 10 m/s
  • With an initial acceleration of 2 m/s²
  • In motion with a speed of 5 m/s
  • From rest (correct)

    • What type of graph can be constructed from the rocket's motion over the time interval 0 to 14 seconds?

  • Both v-t and s-t graphs (correct)
  • Acceleration graph only
  • Only s-t graph
  • Only v-t graph

    • What does the position vector r represent in curvilinear motion?

    <p>The position of the particle at a point in time</p> Signup and view all the answers

    When analyzing erratic motion, at what point is the boat said to stop?

    <p>When the speed reaches 0 m/s</p> Signup and view all the answers

    What does the equation v = ds / dt represent?

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

    How can a v-t graph be constructed from an a-t graph?

    <p>By integrating acceleration over time.</p> Signup and view all the answers

    What is required to determine the velocity at a specific point from a s-t graph?

    <p>The slope of the s-t graph.</p> Signup and view all the answers

    What does the equation a = dv / dt indicate?

    <p>Acceleration is the change in velocity over time.</p> Signup and view all the answers

    In the context of motion, what does the term 'erratic' imply?

    <p>Random and unpredictable changes.</p> Signup and view all the answers

    What does the area under an a-t graph represent?

    <p>The change in velocity.</p> Signup and view all the answers

    Which equation relates acceleration to velocity and displacement?

    <p>ads = v dv</p> Signup and view all the answers

    Which variable must be known to estimate other unknown variables in kinematics?

    <p>One of the variables: s, v, a, or t</p> Signup and view all the answers

    What is the relationship between the radial velocity vr and the radius r given in the equations?

    <p>vr is equal to 0</p> Signup and view all the answers

    What does the equation $a_r = r - rθ^2$ represent?

    <p>Radial acceleration is negative with respect to angular motion</p> Signup and view all the answers

    If one particle moves downwards, what happens to the other particle according to the motion analysis mentioned?

    <p>It moves to the left with twice the downward motion</p> Signup and view all the answers

    What represents the instantaneous velocity of a particle?

    <p>The limit of the change in displacement as time approaches zero</p> Signup and view all the answers

    What remains constant during the motion of the particles in the example provided?

    <p>Length segments lCD and lT</p> Signup and view all the answers

    What is the mathematical expression for instantaneous acceleration?

    <p>a = lim (∆v / ∆t)</p> Signup and view all the answers

    The equation $a_θ = rθ + 2rθ$ simplifies to which of the following?

    <p>$3rθ$</p> Signup and view all the answers

    Which of the following correctly expresses speed?

    <p>v = lim (∆s / ∆t)</p> Signup and view all the answers

    What does the term 'aavg' represent in the context of motion?

    <p>The average acceleration over a specific time interval</p> Signup and view all the answers

    What causes the change in velocity (∆v) of a particle?

    <p>Variance in the force applied to the object</p> Signup and view all the answers

    Which statement best describes a hodograph?

    <p>It is a graph that represents velocity vectors at different points.</p> Signup and view all the answers

    What is the relationship between ∆r and ∆s as ∆t approaches zero?

    <p>∆r approaches the arc length ∆s</p> Signup and view all the answers

    What happens to the average velocity as time interval approaches zero?

    <p>It becomes instantaneous velocity</p> Signup and view all the answers

    What does the equation $a = a_x + a_y + a_z$ represent in the context of motion?

    <p>The total acceleration of the object in three dimensions</p> Signup and view all the answers

    At $t=2$ seconds, what is the horizontal position of the weather balloon if $x=2.4t$?

    <p>4.8 m</p> Signup and view all the answers

    What is the significance of the components $(v_0)_x$ and $(v_0)_y$ in projectile motion?

    <p>They represent the initial velocities in the horizontal and vertical directions</p> Signup and view all the answers

    What is indicated by the equation $y=x^{2/3}$ for the balloon's path?

    <p>A nonlinear relationship between x and y</p> Signup and view all the answers

    For projectile motion with zero horizontal acceleration, which equation is applied?

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

    In the given equations, what does $a_x = v_x = x$ imply about the variables?

    <p>Velocity is defined by the horizontal component of position</p> Signup and view all the answers

    At $t=2$ seconds, if $y=x^{2/3}$, what is the value of y given the previously calculated x?

    <p>10.24</p> Signup and view all the answers

    What is the definition of a direction vector in the context of motion?

    <p>A unit vector representing the object's direction</p> Signup and view all the answers

    Study Notes

    Rectilinear Erratic Motion

    • The motion of an object cannot be described by a single continuous mathematical function, instead, a series of equations are needed
      • velocity, acceleration, and displacement are described
      • v = ds/dt, a = dv/dt, ads = vdv
    • The s-t graph shows the relationship between displacement and time
      • The slope of the s-t graph is the velocity
    • The v-t graph is constructed by plotting the velocity at each instant of time
      • The slope of the v-t graph is the acceleration
    • The a-t graph can be constructed similarly to the v-t graph
    • If the a-t graph is given, the v-t graph can be determined by calculating the area under the a-t graph
      • ∆v = ∫ a dt
      • The change in velocity is equal to the area under the a-t graph

    Work Examples

    • To determine the maximum speed and stopping time of a boat given its acceleration, use the equations of motion.
      • For example, if the boat starts from rest, the initial velocity is zero
    • To determine the v-t and s-t graphs for a rocket given its acceleration, use the equations of motion
      • The rocket is starting from rest

    Curvilinear Motion

    • The position of a particle is defined by the position vector r = r(t)
    • The velocity of a particle is the rate of change of position with respect to time:
      • v = lim (∆r/∆t) = lim (∆s/∆t) as ∆t -> 0
      • v = ds/dt
    • The direction of the velocity vector is tangent to the path of motion
    • The acceleration of a particle is the rate of change of velocity with respect to time:
      • a = lim (∆v/∆t) as ∆t ->0
      • a = dv/dt
    • The acceleration vector has components in the x, y, and z directions:
      • a = axi + ayj + azk

    Curvilinear Motion: Rectangular 3-dimension

    • The horizontal position of a weather balloon can be defined by an equation x = 2.4t (m), where t is in seconds.
    • The magnitude and direction of the balloon's velocity and acceleration can be determined using the equations of motion.
      • Use the equation of the path y=x2/3 to find the y-component of the velocity and acceleration.
    • The balloon's velocity and acceleration at t = 2s can be found using these equations.

    Curvilinear Motion: Projectile Motion

    • A projectile launched at point (x0, y0) with an initial velocity v0 has components (v0)x and (v0)y.
    • The horizontal motion of the projectile is constant acceleration motion because the horizontal acceleration is zero (ax = 0).
    • The vertical motion of the projectile is affected by gravity.
    • The vertical acceleration is -g, which is the acceleration due to gravity.
    • The equations of motion for projectile motion can be used to determine the trajectory of the projectile.

    Dependent Motion Analysis of Two Particles

    • When two particles' motions are interdependent, the equations of motion can be used to analyze the relationship between their positions, velocities, and accelerations.
    • For example, two particles connected by a chord, where the length of the chord remains constant.
    • The motion of one particle affects the motion of the other.
    • As one particle moves up, the other moves to the left, and their velocities are related. The time derivatives of the lengths of the chord segments can be used to determine the relationship.

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    Description

    Explore the principles of rectilinear erratic motion through this quiz. Understand how to analyze displacement, velocity, and acceleration using various graphs. Test your ability to apply equations of motion to real-world examples.

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