Equation Setup
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 5 practice questions.
Before you touch an equation: pick a positive direction, list Δx, v0, v, a, and t with signs, then choose the one equation that leaves out the quantity you don’t know and don’t need.
1. Set up before you solve
Choose + and draw it. Usually the direction of the first motion, or up.
Make a chart: Δx, v0, v, a, t. Fill in what the problem gives you, with signs.
Circle the unknown you want. Cross out the one you don’t know and don’t need.
Pick the equation that leaves out the crossed-out quantity, then solve.
2. Pick the equation by what’s missing
These only work when the acceleration is constant.
3. Example, then try it
A car moving at 20 m/s brakes and stops in 40 m. What is its acceleration?
Chart (+ = direction of motion): v0 = +20 m/s, v = 0, Δx = +40 m, a = ?, t = not needed.
No t, so use v2 = v02 + 2aΔx: 0 = 400 + 2a(40)
a = −400 ÷ 80 = −5 m/s². The minus sign means the acceleration points opposite the motion, as it should for braking.
A ball is thrown straight up at 15 m/s. How long until it is moving downward at 5 m/s? Where is it then? Use g = 10 m/s².
Choose + : up.
Chart: v0 = +15 m/s, v = −5 m/s (moving down), a = −10 m/s², t = ?
Time (no Δx needed): v = v0 + at → −5 = 15 − 10t → t = 2.0 s
Position: v2 = v02 + 2aΔx → 25 = 225 − 20Δx → Δx = +10 m
Answer: after 2.0 s, the ball is 10 m above where it was thrown, on its way down.
4. Common mistakes
A cart starts at 2 m/s and speeds up at 0.5 m/s² for 6 s. You want its displacement. Which equation gets there in one step?
You know v₀, a, and t and want Δx. The final velocity isn’t known or needed, so use the equation without v: Δx = (2)(6) + ½(0.5)(6)² = 12 + 9 = 21 m.
Ready to practice?
5 questions on Equation Setup, each with a hint and an explanation for every wrong answer.