How to Estimate Instantaneous Velocity

Estimation Through Observation

• 1

  Record the object's position at a specific time. Call this T1.

• 2

  Record the objects position at a later time. Call this T2.

• 3

  Divide the distance the object has travelled by the amount of time that elapsed. This will represent the average velocity the object travelled during the time interval. If the object is not accelerating, it will also be equal to the instant velocity at any point during the time interval. If the object is accelerating, this will not be true, but as the time interval is made shorter, the average velocity will become a closer approximation of the instantaneous velocity of the object at either T1 or T2.

Calculation with Known Constant Acceleration

• 4

  Use the formula x = x0 + v0t + ½ at^2 to describe an object moving under constant acceleration. x0 = position at time zero, x = position at any specified time, v0=initial velocity, a = acceleration and t = time. This is the position as a function of time.

• 5

  Take the derivative of the position function to get the velocity as a function of time. This works out to v = v0 +at.

• 6

  Plug your numbers into the equation and solve. Suppose you had an object accelerating under the constant influence of gravity. The acceleration would be 9.8 meters/ sec^2. If the object began at rest at time zero and started falling, and you wanted to know its velocity after 2 seconds, the formula gives you 19.6 meters/second as the instantaneous velocity at 2 seconds.