SPH4U - Unit 1 - Kinematics and Dynamics

Position, Velocity, and Acceleration

• Position - The location of an object at a particular time

• Displacement - The change in position of an object

  • It indicates the final distance and direction moved from a starting position

  • It does not necessarily equal the total distance traveled

• Average Velocity - Displacement divided by time over which displacement occurs

• Instantaneous Velocity - Velocity at a specific instant, or the average velocity over an infinitesimal time interval

• Position-time graphs compare the position of an object, relative to a specific point, to the amount of time passed

  • The vertical axis indicates the position

  • The slope indicates the speed

    • A steeper slope will be moving faster

  • A decreasing slope indicates that the object is moving towards a specific point

  • An increasing slope indicates that the object is moving away from a specific point

  • The instantaneous speed can be calculated by taking the slope of the tangent line at a specific point on the graph

    Position-Time Graph Shape	Type of Motion
    Straight, horizontal line above the x-axis	At rest at a constant positive position Velocity = 0
    Straight, horizontal line below the x-axis	At rest at a constant negative position Velocity = 0
    Straight, upwards, diagonal line	Moving away from reference point Velocity = constant
    Straight, downwards, diagonal line	Moving towards reference point Velocity = constant
    Upward curve that becomes steeper	Accelerating away from reference point Velocity = not constant
    Downward curve that becomes steeper	Accelerating towards reference point Velocity = not constant

• Velocity-time graphs compare the velocity of an object to the amount of time passed

  • The vertical axis indicates the speed

  • If the graph is above the x-axis, it is moving away from a specific point

  • If the graph is below the x-axis, it is moving towards a specific point

    • If moving away from the specific point in one direction is positive, going the opposite direction (towards the point) makes the displacement negative, so the total velocity becomes negative

  • The area between the graph and the horizontal axis shows how far an object travels

  • The slope indicates the acceleration

    • A horizontal line means that it is travelling at a uniform velocity

    • The specific location of the object cannot be determined

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Projectile Motion