Constant Acceleration

The five “SUVAT” equations for motion with constant acceleration. Fill in any three of displacement, start speed, end speed, acceleration and time; the other two are calculated.

MechanicsKinematicsSUVAT

Inputs

Click Use on exactly three values you know. Directions matter: choose a positive direction, and give speeds, displacement and acceleration in the other direction a minus sign (gravity pulling down while you throw up: a = −9.81).

Input examples

Displacement s

Initial velocity u

Final velocity v

Acceleration a

Time t

What is Constant Acceleration?

When the acceleration stays the same, velocity changes by the same amount every second. Free fall (ignoring air), a car braking firmly and a train pulling away smoothly are all close to this.

Five quantities describe such a motion: displacement s, initial velocity u, final velocity v, acceleration a and time t — hence “SUVAT”. Each equation leaves one of them out, so three known values always fix the other two.

a > 0speeding up (if u > 0)

a < 0slowing down

g = 9.81m/s² on Earth

areaunder v–t = s

Velocity–Time Graph

v(t)

velocity v(t) = u + at

area = displacement s

Result

Enter three values above

The Five Equations

Equation	Leaves out

Worked Techniques

Pick the Right Equation

List what you know and what you want. The one quantity that appears in neither list tells you which equation to use.

Example: braking distance without time: use

Braking Distance

Stopping distance grows with the square of the speed: twice as fast needs four times the distance.

Example:

Maximum Height of a Throw

At the highest point the vertical velocity is momentarily zero. Use that as the third known value.

Example:

Sources & Verification

References

D. Halliday, R. Resnick & J. Walker, Fundamentals of Physics, 10th ed., Wiley, 2014 — Ch. 2 (Motion Along a Straight Line).