Linear Motion & Kinematics Study Guide:

DEFINITIONS:

  • Acceleration

    • The rate of change of an objects velocity over time.

      • It measures how quickly an object’s speed or direction is changing.

  • Velocity

    • A vector quantity that describes the rate of change of an objects position over time.

      • Tells you both how fast something is move in and in which direction it’s moving.

  • Displacement

    • Tells you how far something has moved from where it started and in which direction it has moved.

  • Magnitude

    • A term used to refer to the size, extent, or quantity of a physical or mathematical quantity without regard to its direction.

    • It tells you how much of something there is.

  • Kinematic Equations

    • D = Vot+1/2at

    • Vf = Vo+at

    • Vf^2 = Vo^2+2ad

Explain how velocity relates to the distance an object travels over time:

  • Velocity relates to the distance an object travels over time by indicating how fast the object is moving and in which direction.

  • Velocity tells you the rate at which the distance is changing over time

  • Formula: Distance = Velocity x Time

Explain how velocities can be described in space:

  • Velocity can be described in space as the speed and direction at which an object is moving through vastness of outer space

  • It tells you how fast the object is traveling and in which specific path it is moving relative to other objects or reference points in space.

  • Typically measure in unites like kilometers per second (km/s)

Be able to identify where velocity can assessed in a distance vs. time graph and be proficient in articulation of how it looks:

  • Velocity can be assessed by examining the slope of the graph.

  1. Positive Slope: the object is moving away from the starting point. In this case, the object is moving away from the origin.

  2. Negative Slope: the object is moving back toward the starting point, toward the origin.

  3. Zero Slope: the object is at rest

  4. Steepness of the Slope: represents a greater magnitude of velocity (either positive or negative), indicating a faster rather of change.

    1. Exp. “The graph has a steep, negative slope, indicating that the object is moving back toward its starting point at a constant negative velocity.”

Explain how acceleration relates to the velocity and object travels over time:

  • Acceleration relates to the velocity and how an object travels over time by describing how the velocity of the object changes as time goes on.

  • Acceleration tells you how quickly an objects speed or direction is changing while it is in motion.

  • If an object is accelerating, it means that its velocity is not constant; it’s either speeding up, slowing down, or changing direction.

    • Positive acceleration = the object is speeding up

    • Negative acceleration = the object is slowing down

    • Non-zero acceleration = changing direction

Explain how acceleration can be described in space:

  • Acceleration in space is described as the change in an objects speed or direction as it moves through the vast expanse of outer space.

Be able to identify where acceleration can be assessed in a velocity vs. time graph and be proficient in the articulation of how it looks:

  • You’re able to identify acceleration by examining the slope of the graph:

    • A straight line on the graph indicates constant acceleration

    • An upwards line on the graph indicates positive acceleration

    • A negative line on the graph indicates negative acceleration

HOW TO IDENTIFY THE KEY SECTIONS IN PROBLEMS:

  1. Distance -

    1. It’s usually measured in units like meters (m) or kilometers (km)

    2. In a problem look for information related to the total path covered

  2. Acceleration -

    1. Look for information that indicates changes in speed or direction

  3. Initial Velocity -

    1. The objects speed at the beginning of the motion

    2. In a problem search for the velocity at the starting point

  4. Final velocity -

    1. The objects speed at the end of the motion

    2. Look for velocity at the ending point or when the motion stops

IDENTIFY WHAT THESE TERMS MEAN:

  • “At/from rest”

    • From rest is used to describe the initial condition of an object

    • It means it begins its motion to action from a state of complete stillness, or in other words, with an initial velocity of zero

  • “Steps off”

  • “Constant velocity”

    • Refers to a situation in which an object is moving in a straight line and its velocity remain the same over time.

    • It means that both speed and direction are not changing

  • “Neglecting friction”

    • It means we are intentionally ignoring the effects of friction, which is a force that opposes the relative motion or attempt motion of objects in contact

  • “Air resistance is negligible”

    • It means that in any given scenario, the effects of air resistance or drag on an objects motion are so small they can be ignored for the purposes of the analysis.

  • “On earth”

    • The gravity or acceleration is -9.8m/s^2