Calculator Soup^{®}

x = v_{0}t + ½at^{2}

Where:

x = displacement

v_{0} = initial velocity

a = acceleration

t = time

The displacement calculator finds the displacement (distance traveled) by an object using its initial velocity, acceleration, and time traveled. The equation used is x = v0t + ½at2; it is manipulated below to show how to solve for each individual variable.

- x = v
_{0}t + ½at^{2}- x = displacement
- v
_{0}= initial velocity - a = acceleration
- t = time

Solving for the different variables we can use the following formulas:

- Given v
_{0}, t and a calculate x

Given initial velocity, time and acceleration calculate the displacement.- x = v
_{0}t + ½at^{2}

- x = v
- Given x, t and a calculate v
_{0}

Given displacement, time and acceleration calculate the final velocity.- v
_{0}= x/t - ½at

- v
- Given a, v
_{0}and x calculate t

Given acceleration, initial velocity and displacement calculate the time.- ½at
^{2}+ v_{0}t - x = 0

- ½at
- Given x, t and v
_{0}calculate a

Given displacement, time and initial velocity calculate the acceleration.- a = 2x/t
^{2}- 2v_{0}/t

- a = 2x/t

**Displacement Problem 1:** A car traveling at 25 m/s begins accelerating at 3 m/s2 for 4 seconds. How far does the car travel in the 4 seconds?

The three variables needed for distance are given as Vo (25 m/s), A(3 m/s2), and T(4 sec).

x = v0t + ½at2. X=25 (m/s)*4 (sec) + ½*3 (m/s2)*(4 (sec))2= **124 meters**

**Displacement Problem 2: **It takes a plane, with an initial speed of 20 m/s, 8 seconds to reach the end of the runway. If the plane accelerates at 10 m/s2, how long is the runway?

x = v0t + ½at2. X= 20 (m/s)*8(sec)+ ½*10(m/s2) *(8(sec))2 =** 600 meters**

**Cite this content, page or calculator as:**

Furey, Edward "Displacement as a function of Velocity, Acceleration and Time" From *http://www.CalculatorSoup.com* - Online Calculator Resource.