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1.3 Kinematic Equations

Part of Kinematics in AP® Physics C: Mechanics. Read the opening section, then create a free account for the full interactive lesson, practice, and progress tracking.

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Velocity Update Equation

The velocity update equation allows us to find the change in velocity over some period of time. Below are the steps shown to derive it.

  1. First, start with the equation ax=dvxdt{a_x=\frac{dv_x}{dt}}, then separate it into dvx=axdt{dv_x=a_xdt}
  2. Then you can integrate both sides, from some time t=0{t=0} with some velocity vxo{v_{xo}} to some time t{t} with velocity vx{v_x}, resulting in ∫vxovxdvx=∫0taxdt{\int_{v_{xo}}^{v_x}dv_x=\int_{0}^ta_xdt}
  3. Assuming the acceleration is constant, solving the integral gets vx−vxo=axt{v_x-v_{xo}=a_xt}
  4. Using algebraic manipulation, we get vx=vxo+axt{v_x=v_{xo}+a_xt}


vx=vxo+axtv_x=v_{xo}+a_xt
  • vx{v_x} is the final velocity of the object along the x-axis
  • vxo{v_{xo}} is the initial velocity of the object along the x-axis
  • ax{a_x} is the acceleration of the object along the x-axis
  • t{t} is the time interval over which the acceleration occurred

In this unit

6 lessons

  1. 1.1Scalars and VectorsPreview lesson
  2. 1.2Quantifying MotionPreview lesson
  3. 1.3Kinematic EquationsThis lesson
  4. 1.4Graphing MotionPreview lesson
  5. 1.5Relative MotionPreview lesson
  6. 1.6Motion in Two or Three DimensionsPreview lesson

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