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Motion Analysis quiz

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  • What is the relationship between position, velocity, and acceleration in motion analysis?
    Position is s(t), velocity is the first derivative of position (v = ds/dt), and acceleration is the second derivative of position (a = d^2s/dt^2).
  • How do you find the velocity function from a position function?
    Take the first derivative of the position function with respect to time; v(t) = ds/dt.
  • What does the position function s(t) represent in motion analysis?
    It represents the location of an object at a given time t.
  • How is displacement calculated over a time interval?
    Displacement is the final position minus the initial position: s(final) - s(initial).
  • What is the formula for average velocity over a time interval?
    Average velocity is the change in position divided by the change in time: (s(final) - s(initial)) / (t(final) - t(initial)).
  • How do you find instantaneous velocity at a specific time?
    Plug the specific time into the velocity function; v(t) at that time gives the instantaneous velocity.
  • What is the difference between speed and velocity?
    Speed is the absolute value of velocity and always positive, while velocity can be negative or positive depending on direction.
  • How do you calculate speed from velocity?
    Take the absolute value of the velocity; speed = |v|.
  • What is the mathematical definition of acceleration?
    Acceleration is the first derivative of velocity or the second derivative of position with respect to time.
  • How do you find the change in velocity over a time interval?
    Subtract the initial velocity from the final velocity: v(final) - v(initial).
  • What is the formula for average acceleration?
    Average acceleration is the change in velocity divided by the change in time: (v(final) - v(initial)) / (t(final) - t(initial)).
  • What are the units for acceleration in motion analysis?
    Acceleration is measured in distance per squared time, such as meters per second squared (m/s^2).
  • How do you find the acceleration function from a velocity function?
    Take the first derivative of the velocity function with respect to time; a(t) = dv/dt.
  • How do you calculate instantaneous acceleration at a specific time?
    Plug the specific time into the acceleration function; a(t) at that time gives the instantaneous acceleration.
  • What is the difference between average and instantaneous values in motion analysis?
    Average values are calculated over a time interval between two points, while instantaneous values are calculated at a single specific point in time.