Distance - `v_0` and `Delta v`/`Delta t`

The Distance using Change in Velocity calculator computes the distance traveled (Δx) by an object from the origin after a period of time (Δt),  the objects initial velocity (v₀) and a change in velocity (Δv).

INSTRUCTIONS: Choose units and enter the following:

• (t) Duration of Travel
• (V₀) Initial Velocity
• (Δv) Change in Velocity 

Distance Traveled (Δx): The calculator returns the distance traveled in meters.  However, this can be automatically converted into other length or distance units via the pull-down menu.  The calculator also returns the acceleration.

The Math / Science

The Distance Calculator using change in velocity uses the following formula:

       Δx= v₀⋅Δt + ½ Δv/Δt ⋅ Δt²

where:

• Δx = Distance Traveled
• Δt = Duration of Travel
• Δv = Change in Velocity

This equation is a form of the following equation with no initial distance (x₀= 0).  dx = x₀ + v₀•t + ½•a•t² where a = (Δv)/t.

References

• Light and Matter(Dr. Benjamin Crowell) Chapter 3.6 Algebraic results for constant acceleration

Notes

A common application for this equation is the travel associated with the free fall of an object under the force of gravity. In the case of Earth's gravity, the constant acceleration is approximately 9.8 m/s².  Note that this formula does not include other forces such as drag.

See this video discussing a real use for this equation:

https://www.youtube.com/watch?feature=player_embedded&v=z68vta3N5kg