Acceleration Calculator

Acceleration Calculator – Full SUVAT Motion Equations Explained

The Acceleration Calculator on MyTimeCalculator is built around the standard constant-acceleration equations used in physics. These are sometimes called the SUVAT equations, after the symbols for displacement s, initial velocity u, final velocity v, acceleration a and time t. By combining these formulas, the calculator can solve for almost any unknown in straight-line motion with constant acceleration.

On this page you will find several focused tabs and one SUVAT Auto Solver. Each mode uses the same core equations but presents them in a way that matches the type of problem you want to solve.

Core Acceleration and SUVAT Formulas

The basic definition of average acceleration is change in velocity over time:

For constant acceleration in a straight line, you also have four key SUVAT equations:

Each equation links different subsets of s, u, v, a and t. The calculator uses these relationships to solve for unknown quantities when enough inputs are known.

Acceleration from Velocity Change

The Acceleration tab uses the definition of average acceleration:

If the final velocity v is greater than the initial velocity u, the acceleration a is positive and the object is speeding up in the positive direction. If v is smaller than u, a is negative and the object is slowing down (sometimes called deceleration) or speeding up in the opposite direction, depending on how you define positive.

Final Velocity from v = u + at

The Final Velocity tab uses the first SUVAT equation:

This formula starts from the idea that acceleration is the rate of change of velocity. Over a time interval t, a constant acceleration a changes the velocity by at. Adding this change to the initial velocity u gives the final velocity v.

Displacement from s = ut + ½at²

The Displacement tab uses the second SUVAT equation:

The term ut represents the displacement you would get from moving at the initial velocity u for time t. The additional term ½at² accounts for the fact that velocity is changing during the motion when acceleration is nonzero. Together they give the total displacement s in a straight line.

Solving for Time: Linear and Quadratic Equations

There are two common ways to solve for the time t. The simpler case uses the linear equation:

This works when you know u, v and a and acceleration is not zero. When you know displacement instead, you can rearrange s = ut + ½at² into a quadratic equation in t:

This is a quadratic of the form At² + Bt + C = 0 with A = ½a, B = u and C = −s. The solutions are found using the quadratic formula:

In the Time tab, the calculator computes these solutions and shows both possible times when the discriminant is non-negative. Physical problems often use the positive time solution that matches the scenario.

Force and Acceleration from F = ma

In the Force F = ma tab, the calculator uses Newton’s Second Law:

Here F is the net force on an object, m is its mass and a is its acceleration. The same equation can be rearranged to solve for mass or acceleration:

By entering any two of F, m and a, the calculator can find the third. This is useful both for pure physics questions and for engineering problems involving loads and accelerations.

Momentum, Impulse and Average Acceleration

The Momentum & Impulse tab combines the ideas of momentum and impulse. Linear momentum p is defined as:

If an object’s velocity changes from u to v over a time interval Δt, the change in momentum is:

Impulse is defined as force times time, and equals the change in momentum:

Combining these relationships gives an expression for average force and average acceleration:

The calculator uses these formulas to report initial and final momentum, momentum change, average force and average acceleration.

How the SUVAT Auto Solver Combines Equations

The SUVAT Auto Solver tab accepts any combination of s, u, v, a and t. It then applies the four standard SUVAT equations in sequence to fill in missing variables where possible:

For example, if you enter u, a and t, the solver first finds v from v = u + at and then finds s from s = ut + ½at². If you enter s, u and v, it can compute a from v² = u² + 2as and then t from t = (v − u) ÷ a. By running several passes of these relationships, the calculator constructs a consistent set of s, u, v, a and t whenever the inputs allow it.

Units and Consistency

The formulas in this Acceleration Calculator work as long as you use consistent units. The standard choice is SI units:

• Displacement s in meters (m)
• Velocities u and v in meters per second (m/s)
• Time t in seconds (s)
• Acceleration a in meters per second squared (m/s²)
• Mass m in kilograms (kg)
• Force F in newtons (N)

If you prefer other units, you can still use the calculator, but all inputs must be in compatible units so that the formulas remain valid.

How to Use the Acceleration Calculator Step-by-Step

• Choose the tab that matches your problem: Acceleration, Final Velocity, Displacement, Time, Force, Momentum or SUVAT Auto Solver.
• Enter the known values in the input boxes, leaving unknown quantities blank where appropriate.
• Click the calculate button on that tab to see results in the summary cards.
• Check the formula text under each mode to see which equation was used to compute your result.
• Use the SUVAT Auto Solver when you have several pieces of information about a motion and want the calculator to fill in the rest.

This combination of focused solvers and a general SUVAT engine makes it easier to explore motion problems, check homework and build intuition about how acceleration, velocity, displacement and time fit together.