Velocity Calculator v = u + at
Solve for final velocity, initial velocity, acceleration or time using the formula v equals u plus a times t.
| Quantity | Value | Unit |
|---|
Standard gravity value for velocity problems
Standard gravity value is used whenever a problem involves an object falling or rising under Earth’s gravitational pull, and it appears as a fixed acceleration constant in the equation.
| Constant | Value | Unit |
|---|---|---|
| Standard gravity (g) | 9.80665 | m/s² |
| Standard gravity (g) | 32.174 | ft/s² |
The velocity equation explained
The velocity equation states that v equals u plus a times t, where v is final velocity, u is initial velocity, a is acceleration and t is the elapsed time. This formula assumes constant acceleration throughout the entire time interval.
If you know any three of the four variables, this calculator solves for the remaining one using one of the following rearranged formulas.
Solving for initial velocity
Solving for initial velocity requires subtracting the product of acceleration and time from final velocity, expressed as u equals v minus a times t. This formula reveals how fast an object was moving before acceleration began.
Solving for acceleration
Solving for acceleration requires subtracting initial velocity from final velocity and dividing by time, expressed as a equals v minus u divided by t. A negative result indicates deceleration.
Solving for time
Solving for time requires subtracting initial velocity from final velocity and dividing by acceleration, expressed as t equals v minus u divided by a. This formula calculates how long it takes for a velocity change to occur.
Worked example using a school zone car
Worked example calculations make the velocity formula easier to apply in real situations. Consider a car approaching a school zone that slows from 27 m/s to 9 m/s with a constant acceleration of negative 2 m/s squared.
Using t equals v minus u divided by a, the calculation becomes 9 minus 27 divided by negative 2, which equals 9 seconds. This means the car needed 9 seconds to slow down to its final velocity.
Frequently asked questions about velocity
The formula is v equals u plus a times t, where v is final velocity, u is initial velocity, a is acceleration and t is time. This calculates final velocity assuming constant acceleration.
To calculate final velocity, add the product of acceleration and time to the initial velocity, using v equals u plus a times t. For example, starting at 0 m/s with acceleration 2 m/s squared for 5 seconds gives a final velocity of 10 m/s.
Standard gravity is 9.80665 meters per second squared. This value is used for problems involving objects falling or being thrown under Earth’s gravitational pull.
Time equals the difference between final velocity and initial velocity divided by acceleration, written as t equals v minus u divided by a. This rearranges the original velocity equation to solve for time.
Acceleration equals the difference between final velocity and initial velocity divided by time, written as a equals v minus u divided by t. This shows how quickly velocity changes over a given time period.
Yes. Negative acceleration represents deceleration, such as a car slowing down, and the formula v equals u plus a times t still applies with a negative value entered for acceleration.