Constant Acceleration Distance Calculator

How it is calculated

The tool uses the two constant-acceleration equations d = v0·t + ½·a·t² and v = v0 + a·t. Here v₀ is the starting velocity in m/s, a the acceleration in m/s² and t the time in seconds. Results are in metres and metres per second, with two decimals. Velocity and acceleration may be negative, which models motion in the opposite direction or braking, but time must be zero or more; a negative time shows no result. A result is also refused if the starting or final speed would reach the speed of light (299,792,458 m/s). The distance is a net displacement, not a path length: the formula does not stop the motion when speed reaches zero, so a braking object that has already stopped is shown moving backwards. It assumes the acceleration stays exactly constant.

Common mistakes

• Dropping the square on the time in the acceleration term. The ½at² part grows with t², so doubling the time quadruples that term.
• Mixing units, such as speed in km/h with acceleration in m/s². Convert speed to m/s first: 72 km/h is 20 m/s.
• Using the formula past the stopping time. For 20 m/s and −4 m/s² over 8 s the tool shows a distance of 32.00 m and a final velocity of −12.00 m/s, because the object would have stopped after 5 s at 50 m and then been pushed backwards.
• Entering a deceleration as a positive number. Braking needs a negative acceleration, otherwise the object speeds up.
• Entering a negative time to look backwards. Time must be zero or more; to look at the past, reverse the sign of the velocity instead.