# Displacement Calculator s = (1/2)( v + u )t

## Calculator Use

This 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 + u)t** can be manipulated, as shown below, to find any one of the four values if the other three are known.

## Displacement Equations for these Calculations:

Where:

s = displacement

v = final velocity

u = initial velocity

t = time

Different resources use slightly different variables so you might also encounter this same equation with v_{i} or v_{0} representing initial velocity (u) and v_{f} representing final velocity (v) such as in the following form:

Where:

s = displacement

v_{f} = final velocity

v_{i} = initial velocity

t = time

## Displacement calculations used in calculator:

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

- Given v, u and t solve for s

Given initial velocity, final velocity and time calculate the displacement.- s = ½( v + u )t

- Given s, t and u solve for v

Given displacement, time and initial velocity calculate the final velocity.- v = 2s/t - u

- Given s, t and v solve for u

Given displacement, time and final velocity calculate the initial velocity.- u = 2s/t - v

- Given v, u and t solve for s

Given initial velocity, final velocity and time calculate the displacement.- t = 2s/ ( v + u )

### Displacement Problem 1:

A car traveled down a road for 45 seconds. The car turned onto 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. s = ½(20+23)*45=
**967.5 meters**

### Displacement Problem 2:

When a pitcher throws a pitch from the pitcher's mound, he is about 60 feet 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 s = ½( v + u )t can be algebraically manipulated to t = 2s/(v+u). 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**