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1.2 Displacement, Velocity, and Acceleration

Syllabus
2024
Topic
1.2
Level
—

Learning objectives

1.2A—Describe a change in an object’s positionDescribe a change in an object’s position.• When using the object model, the size, shape, and internal configuration are ignored. The object may be treated as a single point with extensive properties such as mass and charge.• Displacement is the change in an object’s position. Relevant equation:1.2B—Describe the average velocity and acceleration of an objectDescribe the average velocity and acceleration of an object.• Averages of velocity and acceleration are calculated considering the initial and final states of an object over an interval of time.• Average velocity is the displacement of an object divided by the interval of time in which that displacement occurs.• Average acceleration is the change in velocity divided by the interval of time in which that change in velocity occurs.• An object is accelerating if either the magnitude and/or direction of the object’s velocity are changing. TOPIC 1.2 Displacement, Velocity, and Acceleration• Calculating average velocity or average acceleration over a very small time interval yields a value that is very close to the instantaneous velocity or instantaneous acceleration.1.2C—Describe the instantaneous position, velocity, and acceleration of an object as a function of timeDescribe the instantaneous position, velocity, and acceleration of an object as a function of time.• As the time interval used to calculate the average value of a quantity approaches zero, the average value of that quantity approaches the value of the quantity at that instant, called the instantaneous value.- i. Instantaneous velocity is the rate of change of the object’s position, which is equal to the derivative of position with respect to time. Relevant equations:  dr v= dt dxvx = dt- ii. Instantaneous acceleration is the rate of change of the object’s velocity, which is equal to the derivative of velocity with respect to time. Relevant equations:  dv a= dt dvax = x dt• Time-dependent functions and instantaneous values of position, velocity, and acceleration can be determined using differentiation and integration.

1.2.A—Describe a change in an object’s position

Describe a change in an object’s position.

  • When using the object model, the size, shape, and internal configuration are ignored. The object may be treated as a single point with extensive properties such as mass and charge.
  • Displacement is the change in an object’s position. Relevant equation:

1.2.B—Describe the average velocity and acceleration of an object

Describe the average velocity and acceleration of an object.

  • Averages of velocity and acceleration are calculated considering the initial and final states of an object over an interval of time.
  • Average velocity is the displacement of an object divided by the interval of time in which that displacement occurs.
  • Average acceleration is the change in velocity divided by the interval of time in which that change in velocity occurs.
  • An object is accelerating if either the magnitude and/or direction of the object’s velocity are changing. TOPIC 1.2 Displacement, Velocity, and Acceleration
  • Calculating average velocity or average acceleration over a very small time interval yields a value that is very close to the instantaneous velocity or instantaneous acceleration.

1.2.C—Describe the instantaneous position, velocity, and acceleration of an object as a function of time

Describe the instantaneous position, velocity, and acceleration of an object as a function of time.

  • As the time interval used to calculate the average value of a quantity approaches zero, the average value of that quantity approaches the value of the quantity at that instant, called the instantaneous value.
    • i. Instantaneous velocity is the rate of change of the object’s position, which is equal to the derivative of position with respect to time. Relevant equations:  dr v= dt dxvx = dt
    • ii. Instantaneous acceleration is the rate of change of the object’s velocity, which is equal to the derivative of velocity with respect to time. Relevant equations:  dv a= dt dvax = x dt
  • Time-dependent functions and instantaneous values of position, velocity, and acceleration can be determined using differentiation and integration.