The uniform acceleration equation: v^2 - u^2 = 2as

In this lesson

Apply final velocity squared minus initial velocity squared = 2 x acceleration x distance to an object moving with uniform acceleration, and recall the acceleration of an object in free fall.

What it covers

• The four quantities and their symbols, each with its unit: final velocity v, initial velocity u, acceleration a, distance s
• The equation in words and in symbols: final velocity squared minus initial velocity squared = 2 x acceleration x distance, v^2 - u^2 = 2 a s
• THAT IT IS GIVEN, NOT RECALLED - it is on the equation sheet of all three boards, so the marks are for selecting it, rearranging it and finishing it, never for remembering it
• WHEN to select it: the question gives you a distance and no time, or asks for a distance and gives you no time. That is the whole selection rule.
• The boards' printed limiter, carried from the atom next door: uniform acceleration only
• Each rearrangement written on its own line before any substitution: a = (v^2 - u^2) / 2s, s = (v^2 - u^2) / 2a, and v = the square root of (u^2 + 2as)
• THE SQUARE ROOT AS ITS OWN VISIBLE STEP, always the last line, never folded into the substitution
• The from-rest case, u = 0, and why u^2 then vanishes rather than being ignored
• A deceleration substituted as a negative acceleration, and what a negative answer means
• The acceleration of an object in free fall near the Earth's surface, used as the value of a in a dropped-object question - AND the fact that the boards print different values for it, so the value to use is the one on your board's sheet or in the question (see the board_truth block and concern PH02-C3)
• The relationship, not just the sum: with the same deceleration, doubling the starting speed makes the stopping distance FOUR times as long, because the speed is squared

Key words

On the specification