The Distance Traveled at Constant Acceleration calculator computes the distance traveled (dx) by an object after a period of time (t), based on its initial distance from the origin (x), the object's initial velocity (V) and a constant acceleration (a).

INSTRUCTIONS: Choose units and enter the following:

• (x₀) Initial Displacement
• (V₀) Initial Velocity
• (a) Constant acceleration
• (t) Duration of Travel

Distance(dx): 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 Math / Science

The formula for the distance traveled with constant acceleration is:
     dx = x+v⋅t+½⋅a·t²
where:

• dx is the distance traveled under constant acceleration
• x is the initial distance
• v is the initial velocity
• a is the constant acceleration
• t is the time of travel.

Application

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 9.80665 m/s².  Note that this formula does not include other forces such as drag.

Motion Calculators:

• Compute Duration (Time) of Free Fall
• Compute Distance (Height) of Free Fall
• Compute Final Velocity of a Free Fall
• Compute the time from the distance and velocity.
• Compute the velocity from the distance and time.
• Compute the distance from the velocity and time.
• Distance from initial displacement, velocity and time
• Distance from initial displacement, velocity, time and constant acceleration

Notes

See this video discussing a real use for this equation:

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

See Also

• Force of Drag - equation for the effect (force) of drag
• Vector Calculator (3D) - vector calculator in 3D
• Motion Calculator - calculator with equations related to motion.