Enter three of initial speed, final speed, acceleration, time and displacement and get the other two from the equations of motion.
m/s
m/s
m/s²
s
m
Enter the values to see the result here.
Formula
For constant acceleration a, with initial speed u, final speed v, time t and displacement s:
v=u+ats=ut+21at2s=2u+vtv2=u2+2as
Pick the set of three known quantities and the tool uses the right pair of equations for the rest.
Worked example
A car moving at 30 m/s brakes at −6m/s2. How far does it travel before stopping?
Known: u=30, v=0, a=−6.
v2=u2+2as gives 0=900−12s, so s=75 m.
Time: t=(v−u)/a=(0−30)/(−6)=5 s.
Doubling the speed to 60 m/s quadruples the stopping distance to 300 m.
Common mistakes
Using the equations when the acceleration changes, for example a car pulling away with the throttle pressed harder.
Mixing units: km/h with m/s². Convert speeds to m/s first.
Entering a deceleration as a positive number. A braking car has a negative acceleration.
Forgetting that s is displacement, not total distance, when the motion reverses.
Frequently asked questions
When do these equations apply?
Only when the acceleration is constant, as for a car braking evenly, a falling object near Earth's surface (a = 9.81 m/s²) or a ball rolling down a smooth slope. For changing acceleration you need calculus.
What does a negative value mean?
Signs show direction. Choose one direction as positive; a negative acceleration is a slowing down in that direction or a speeding up in the opposite one. A negative displacement means the object ended up behind its start.
Why does the u, a, s case give a positive final speed only?
The equation v² = u² + 2as has two roots, ±v. The tool reports the speed as positive. If the object turns around, as when a ball is thrown upward, the same distance can be passed twice, so treat that case with care.