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Questions and Answers

What is the relationship between displacement, velocity, and acceleration?

  • Acceleration is the derivative of displacement with respect to time. (correct)
  • Velocity is the derivative of acceleration with respect to time.
  • Velocity is the integral of displacement with respect to time.
  • Displacement is the integral of acceleration with respect to time. (correct)
  • If a person is moving through levels represented by 'f', 'v', and 'x' or 'y', what does 'f', 'v', and 'x' or 'y' represent?

  • Acceleration, displacement, and force respectively.
  • Displacement, velocity, and acceleration respectively. (correct)
  • Force, velocity, and displacement respectively.
  • Position, speed, and direction respectively.
  • How would you mathematically express acceleration in terms of velocity and displacement?

  • Acceleration is the square of velocity divided by displacement.
  • Acceleration equals the integral of velocity with respect to displacement.
  • Acceleration is the change in velocity divided by the change in time. (correct)
  • Acceleration is equal to the product of velocity and displacement.
  • What operation is performed on velocity to obtain displacement?

    <p>Integration.</p> Signup and view all the answers

    Which of the following correctly describes differentiation in the context of motion?

    <p>It is used to determine the instantaneous rate of change of a function.</p> Signup and view all the answers

    What is the quadratic equation derived from the equation v = 50 when substituted into 6t^2 + 8t + 10?

    <p>3t^2 + 4t - 20 = 0</p> Signup and view all the answers

    Which factorization correctly represents the quadratic equation 3t^2 + 4t - 20 = 0?

    <p>(3t + 10)(t - 2) = 0</p> Signup and view all the answers

    What are the possible values of t when solving the equation 3t^2 + 4t - 20 = 0?

    <p>t = -3 and t = 2</p> Signup and view all the answers

    What happens to the negative root found in the equation 3t^2 + 4t - 20 = 0?

    <p>It's discarded or rejected.</p> Signup and view all the answers

    What is the value of t when v is equal to 50 in the quadratic equation presented?

    <p>t = 2</p> Signup and view all the answers

    Study Notes

    Mechanics "M151" (Natural Science)

    • This course covers Statics and Dynamics.
    • Note Number (5) is about Kinematic of Motion.

    Kinematic of Motion

    • Kinematics is a subfield of classical mechanics that describes a particle's motion without considering the forces causing the motion.

    • Key aspects of motion include displacement, velocity, and acceleration.

    • Displacement (x or y) is a function of time (t).

    • Velocity (v) is the rate of change of displacement with respect to time (dv/dt or dx/dt).

    • Acceleration (f) is the rate of change of velocity with respect to time (dv/dt).

    • Acceleration can be expressed as a function of displacement or velocity.

    • To find Velocity or displacement, differentiation is used

    • To find acceleration, Integration is used

    • The sign of acceleration (positive or negative) depends on the direction of motion relative to a chosen origin. Positive values indicate motion in the positive direction and negative in the opposite direction.

    • Initial Conditions are vital in determining constants of integration.

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    M151 Note (5) Kin OF Motion PDF

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