time for distance with constant acceleration

The Travel Duration Time (Δt) equation, (`Δt = sqrt((2Δx)/a)`) ,  computes time required to travel a distance (Δx) based on a constant acceleration (a) from an initial velocity of zero.

INSTRUCTIONS:  Choose units and enter the following:

• (Δx) Distance Travelled
• (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 = sqrt(2*(Deltax)/a)`

where:

• Δt = travel time
• Δx = distance travelled
• a = constant acceleration

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.