# Velocity as a Function of Acceleration and Time

## Calculator Use

This velocity calculator uses the equation that the final velocity of an object is equal to its initial velocity added to its acceleration multiplied by time of travel. This calculator does assume constant acceleration during the time traveled. This calculator can be used to find initial velocity, final velocity, acceleration, or time as long as three of the variables are known.

## Velocity Equation in these calculations:

Final velocity (v) of an object equals initial velocity (u) of that object plus acceleration (a) of the object times the elapsed time (t) from u to v.

\[v = u + at \]Where:

u = initial velocity

v = final velocity

a = acceleration

t = time

Use standard gravity, a = 9.80665 m/s^{2}, for equations involving the Earth's gravitational force as the acceleration rate of an object.

## Formula for velocity as a function of initial velocity, acceleration and time

- v = u + at
- u = initial velocity
- v = final velocity
- a = acceleration
- t = time

### Example: Find time (t) given final velocity (v), initial velocity (u) and acceleration (a)

A car approaching a school zone slows down from 27 m/s to 9 m/s with constant acceleration -2 m/s^{2}.

How much time is required to slow down to final velocity?

**Answer**: We know initial velocity (u = 27), velocity (v = 9) and acceleration (a = -2)

We first need to solve the velocity equation for time (t):

v = u + at

v - u = at

(v - u)/a = t

Plugging in the known values we get,

t = (v - u)/a

t
= (9 m/s - 27 m/s) / -2 m/s^{2}

t
= -18 m/s / -2 m/s^{2}

t
= 9 s

## Velocity calculations solved for different variables and used in this calculator:

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

- Given u, a and t calculate v

Given initial velocity, acceleration and time calculate the velocity.- v = u + at

- Given v, a and t calculate u

Given velocity, acceleration and time calculate the initial velocity.- u = v - at

- Given v, u and t calculate a

Given velocity, initial velocity and time calculate the acceleration.- a = (v - u)/t

- Given v, u and a calculate t

Given velocity, initial velocity and acceleration calculate the time.- t = (v - u)/a

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

Furey, Edward "Velocity as a Function of Acceleration and Time"; from *http://www.calculatorsoup.com* - Online Calculator Resource.