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.