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How to Find Acceleration in Calculus

Acceleration indicates the rate at which the velocity of an object -- a car, for example --- changes. Acceleration is measured in units of meter/square seconds. In calculus, the acceleration is defined as the first derivative of the velocity or as the second derivative of the equation of the motion of an object. Calculating acceleration is a common assignment in physics.

Instructions

- 1
  Write down the equation of the motion of an object that describes the position denoted as "X" as a function of time (t). For example, X(t) = 7t^2 -3t + 9.
- 2
  Find the first derivative of the equation of the motion. In this example, the first derivative denoted as X is:
  
  X'(t) = 7x2 t - 3 = 14t -3.
  
  This equation describes the velocity of the object with time.
- 3
  Find the second derivative of the equation of the motion to determine the acceleration. In this example, the acceleration is:
  
  X''(t) =(14t -3)' = 14.

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