Kinematics (DP IB Analysis & Approaches (AA))

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  • Define the term kinematics.

    Kinematics is the branch of mathematics that models and analyses the motion of objects.

  • What is displacement?

    Displacement is the distance of an object in a particular direction (positive or negative) from a fixed point.

  • True or False?

    Displacement can be negative.

    True.

    Displacement can be negative.

  • What is velocity?

    Velocity is the rate of change of displacement at time t.

  • What is speed in the context of kinematics?

    In the context of kinematics, speed is the magnitude (absolute value) of velocity.

  • What is acceleration?

    Acceleration is the rate of change of velocity at time t.

  • True or False?

    A particle at rest always has zero acceleration.

    False.

    A particle at rest has zero velocity, but may have non-zero acceleration.

  • What does "at rest" imply about a particle's velocity?

    At rest implies that the particle's velocity is zero.

  • What does the gradient of a velocity-time graph represent?

    The gradient of a velocity-time graph represents acceleration.

  • True or False?

    Constant acceleration is always indicated on a velocity-time graph by a horizontal line.

    False.

    Constant acceleration is not always indicated on a velocity-time graph by a horizontal line.

    Constant acceleration is indicated by any straight line on a velocity-time graph.

    A horizontal line on a velocity-time graph indicates constant velocity (as well as a constant acceleration of zero).

  • What does the area under a velocity-time graph represent?

    The area under a velocity-time graph represents displacement.

  • True or False?

    Deceleration (slowing down) occurs when a particle's velocity and acceleration have the same sign.

    False.

    Deceleration (slowing down) occurs when a particle's velocity and acceleration have different signs.

  • What does a velocity-time graph crossing the x-axis indicate?

    A velocity-time graph crossing the x-axis indicates the object is stationary at that time.

  • When using calculus for kinematics, what is the equation for velocity in terms of displacement?

    The equation for velocity in terms of displacement is v equals fraction numerator straight d s over denominator straight d t end fraction.

    Velocity is the derivative of displacement.

  • When using calculus for kinematics, what is the equation for acceleration in terms of velocity?

    The equation for velocity in terms of displacement is a equals fraction numerator straight d v over denominator straight d t end fraction.

    Acceleration is the derivative of velocity.

  • Define the second derivative of displacement?

    The second derivative of displacement is acceleration.

    This can be written as a equals fraction numerator straight d squared s over denominator straight d t squared end fraction.

  • True or False?

    Velocity is the antiderivative of acceleration.

    True.

    Velocity is the antiderivative of acceleration.

  • What does the integral of velocity with respect to time represent?

    The integral of velocity with respect to time represents displacement.

  • True or False?

    The distance travelled is always equal to the displacement.

    False.

    The distance travelled is equal to the integral of the absolute value of velocity.

  • What is a boundary condition in kinematics?

    A boundary condition is information given about an object at a specific time.

  • What is an initial condition in kinematics?

    An initial condition is information given about an object at time t equals 0.

    An initial condition is a type of boundary condition.

  • What does integral subscript t subscript 1 end subscript superscript t subscript 2 end superscript v open parentheses t close parentheses space straight d t represent in kinematics?

    integral subscript t subscript 1 end subscript superscript t subscript 2 end superscript v open parentheses t close parentheses space straight d t represents the displacement of the particle between times t₁ and t.

  • What does integral subscript t subscript 1 end subscript superscript t subscript 2 end superscript open vertical bar v open parentheses t close parentheses close vertical bar space straight d t represent in kinematics?

    integral subscript t subscript 1 end subscript superscript t subscript 2 end superscript open vertical bar v open parentheses t close parentheses close vertical bar space straight d t represents the distance travelled by the particle between times t₁ and t.

  • How can you find the constant of integration in kinematics problems?

    The constant of integration in kinematics problems can be found by substituting known values from initial or boundary conditions.

  • True or False?

    The area under a velocity-time graph can be negative.

    True.

    The area under a velocity-time graph can be negative, representing displacement in the negative direction.