Time for Distance with Velocity and Acceleration

WARNING: THIS CALCULATOR IS STILL IN DEVELOPMENT

The Travel Duration Time (Δt) calculator  computes time required to travel a distance based on a constant acceleration and initial velocity.

INSTRUCTIONS:  Choose units and enter the following:

• (Δx) Distance Travelled
• (v) Initial Velocity
• (a) Constant Acceleration

Travel Duration Time (Δt): The calculator returns the duration in seconds.  However this can be automatically converted to other duration units via the pull-down menu.

The Math / Science

The formula for the time required to travel a distance under constant acceleration, with zero initial velocity, is:

`Δt = (-v +- sqrt(v^2 - 2aDeltax))/a`

where:

• Δt = travel time
• Δx = distance travelled
• v = initial velocity
• a = constant acceleration

The above formula is a form of the following:

`Deltax = v*t + 1/2 * a * t^ 2`

The formula used in this calculator is the above formula solved for t using the quadratic equation.

References

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

Notes:

This answers the question, "How long will it take me to free fall a certain distance."  Use, 1 grav (9.8 m/s²) as the value of a.

Note: at zero acceleration (a = 0), it requires infinite time to realize the change in velocity.  This is made mathematically obvious because a is in the denominator and would produce a divide by zero condition which always produces infinity.