SUVAT calculator: equations of motion with working

Each equation leaves out one of the five quantities. List what you know and what you want, then pick the equation without the quantity you don't know and don't need:

• Dropped ball: $u = 0$, $a = 9.8$ m/s², $t = 3$ s. $v = 0 + 9.8 \times 3 = 29.4$ m/s and $s = 0 + \tfrac{1}{2} \times 9.8 \times 3^2 = 44.1$ m.
• Braking car: $u = 20$ m/s, $v = 0$, $s = 40$ m. From $v^2 = u^2 + 2as$: $0 = 400 + 80a$, so $a = -5$ m/s². Then $t = (0 - 20) \div (-5) = 4$ s.

Pick one direction as positive and stick to it. A car slowing down has a negative acceleration; a ball thrown upwards with upwards as positive has $a = -9.8$ m/s². When an answer comes from a square root, the calculator takes the positive value: if the object moves the other way, give it a minus sign yourself.

Braking distance questions are SUVAT questions: final velocity 0, deceleration from the brakes. The braking distance rises with the square of the speed, so doubling the speed makes it four times longer. Add the thinking distance (speed × reaction time) for the total stopping distance; see our stopping distance questions.

• Using SUVAT when the acceleration isn't constant.
• Mixing signs (a decelerating object with a positive $a$).
• Forgetting that "dropped" or "starts from rest" means $u = 0$.

Practise with our SUVAT questions and the acceleration calculator.

• Write the five letters down the side of your working and fill in what you know.
• Free-fall questions: $a = 9.8$ m/s² downwards (some questions use 10). Choose up or down as positive.
• If a quadratic in $t$ appears, solve it and choose the positive time that makes sense.
• Check the answer: a ball dropped for 3 s falls about 44 m, not 440 m.