Here is a subway train pulling away from a platform. Its cab display shows one stretch of the run: in at 4 m/s, out at 10 m/s, 6 s elapsed. How far did the train move in that stretch?
A subway train's cab display: in at 4 m/s, out at 10 m/s, 6 s elapsed. The acceleration is nowhere on it.
Every equation you've seen so far needs the acceleration — and the display never shows one.
First, write down the values from the question, and mark the one you want.
We have v₀, v, and t, but not a — and v = v₀ + at, Δx = v₀t + ½at², and v² = v₀² + 2aΔx all need a. There is a fourth equation for exactly this.
Read ½(v₀ + v) as one piece: ½(4 + 10) = 7 m/s, the average of the starting and final velocities.
A speedboat speeds up steadily from 6 m/s to 16 m/s during a 4 s burst. In Δx = ½(v₀ + v)t, what value does the bracket ½(v₀ + v) take for this burst?
The units combine as a velocity times a time: (m/s) × s = m, so Δx comes out in meters.
The acceleration appears nowhere in it. Reach for this equation when a problem never mentions the acceleration.
Which quantity appears nowhere in Δx = ½(v₀ + v)t?
Your turn
Which statement about Δx = ½(v₀ + v)t is correct?
The bracket ½(v₀ + v) carries the unit m/s. After it is multiplied by the time t in s, which unit does Δx carry?
A boat passes a harbor mouth at 3 m/s and is moving at 9 m/s when it passes a breakwater 20 s later. No acceleration is given. Which kinematic equation finds the boat's displacement from exactly these numbers?