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x = ½( v + v_{0} )t

Where:

x = displacement

v = velocity

v_{0} = initial velocity

The displacement calculator finds the displacement (distance traveled) by an object using its initial and final velocities as well as the time traveled. The average velocity of the object is multiplied by the time traveled to find the displacement. The equation **x = ½( v + v0 )t** can be manipulated, as shown below, to find any one of the four values if the other three are known.

- x = ½( v + v
_{0})t- x = displacement
- v = velocity
- v
_{0}= initial velocity - t = time

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

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

Given initial velocity, final velocity and time calculate the displacement.- x = ½( v + v
_{0})t

- x = ½( v + v
- Given x, t and v
_{0}calculate v

Given displacement, time and initial velocity calculate the final velocity.- v = 2x/t - v
_{0}

- v = 2x/t - v
- Given x, t and v calculate v
_{0}

Given displacement, time and final velocity calculate the initial velocity.- v
_{0}= 2x/t - v

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

Given initial velocity, final velocity and time calculate the displacement.- t = 2x / ( v + v
_{0})

- t = 2x / ( v + v

**Displacement Problem 1:** A car is traveling down a road for 45 seconds. The car turned on to the street at 20 m/s and by the end of the street it was traveling 23 m/s. How long is the street?

Since we were given the initial velocity (20 m/s), the final velocity (23 m/s), and the time (45 seconds) the equation can be directly applied. X= ½(20+23)*45= **967.5 meters**

**Displacement Problem 2:** When a pitcher throws a pitch, he is about 60 ft from home plate. If the ball leaves his hand at 132 ft/s and reaches home plate with a speed of 110 ft/s, how long does it take the ball to travel from the mound to home plate?

In this problem we are given a different set of values. The equation x = ½( v + v0 )t can be algebraically manipulated to t=2x/(v+vo). The displacement is 60 feet, the initial velocity is 132 ft/s and the final velocity is 110 ft/s.

T=2(60 ft)/(132+110 ft/s)= **0.496 seconds**

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

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