The Travel Duration at Constant Acceleration 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 at Constant Acceleration (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.
Motion Calculators:
- Duration (Time) of Free Fall
- Distance (Height) of Free Fall
- Final Velocity of a Free Fall
- Time from the distance and velocity.
- Travel Duration at Constant Acceleration
- Velocity from the distance and time.
- Distance from the velocity and time.
- Distance from initial displacement, velocity and time
- Distance from initial displacement, velocity, time and constant acceleration