1.2 Displacement, Velocity, and Acceleration

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:

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.

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.