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Uniformly Accelerated Motion Calculator

Uniformly Accelerated Motion
initial velocity
final velocity
v =
units
displacement
acceleration
time
t =
units
Answer:
v = 27039919.532973 km/h
final velocity

t = 212.89935827795 h
time


Derived Equations for Solution:
\( v = \sqrt{ u^2 + 2as } \)
\( t = \dfrac{v - u}{a} \)
These derived equations are one example. You can usually derive more than one set of equations to solve your problem in different ways.

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Calculator Use

The Uniformly Accelerated Motion calculator or (kinematic equations calculator) solves motion calculations involving constant acceleration in one dimension, a straight line. It can solve for the initial velocity u, final velocity v, displacement s, acceleration a, and time t.

Choose a calculation to find the variables that are unknown and enter the variables that are given in your problem. This calculator will calculate the unknown values and provide the derived equations that were used to find the solution. Solution equations are derived from the uniformly accelerated motion equations below.

Note that when solving for multiple variables there is usually more than one way to solve for your unknowns. You can derive more than one set of equations to solve your problem in different ways.

Uniformly Accelerated Motion Equations

Kinematic Equations

\( s = \dfrac{1}{2}(v + u)t \)
Equation 1
\( v = u + at \)
Equation 2
\( v^2 = u^2 + 2as \)
Equation 3
\( s = ut + \dfrac{1}{2}at^2 \)
Equation 4

Where:

  • u = initial velocity
  • v = final velocity
  • a = acceleration
  • s = displacement
  • t = time

Use standard gravity, a = 9.80665 m/s2, for equations involving the Earth's gravitational force as the acceleration rate of an object.

Equations 1 through 4 are the key equations used to solve for variables in this calculator however you will sometimes see a different number of Uniformly Accelerated Motion Equations depending on the resource. You will find that equation 1 comes from substituting equation 1b into equation 1a below.

\( s = \overline{v}t \)
Equation 1a
\( \overline{v} = \dfrac{1}{2}(v + u) \)
Equation 1b
 

Last updated: October 11, 2023

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