Equations of uniformly accelerated motion
3 marks · NormalExplain, using an example, when you would use the equation v^2 = u^2 + 2as instead of the equation v = u + at to solve a problem about an object's motion.
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You use v^2 = u^2 + 2as when the time (t) is not known but you are given or can find the initial speed (u), acceleration (a), and distance moved (s), and you need to find the final speed (v) or another of the variables. For example, if a stone falls from a height and you know how far it dropped and its starting speed, but you don't know the time, you would use this formula.
Must show: Identifies that v^2 = u^2 + 2as is used without time, Provides a suitable example context, Contrasts with v = u + at
Also accept: You use v^2 = u^2 + 2as when distance not time is known; The formula is used for motion with uniform acceleration when information about distance, speed, and acceleration is given but not time
Common mistakes: Saying the two equations are interchangeable without describing when to use each; Giving an example without explanation
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Marking points
B1 · 1 mark · States v^2 = u^2 + 2as is used when time is not known.
B2 · 1 mark · Contrasts with v = u + at, which is used when time is known.
B3 · 1 mark · Provides an appropriate example for v^2 = u^2 + 2as (e.g., falling object where distance is known but not time).
Worked solution
You use v^2 = u^2 + 2as when you do not know the time taken but you do know the distance, initial speed, and acceleration, and wish to find the final speed (or another variable from the equation). For example, if a ball is thrown straight up and you know how high it rises before stopping, but not how long it takes, you can use v^2 = u^2 + 2as to calculate the initial speed or maximum height.
By contrast, v = u + at is used when you know the acceleration and the time for which it acts.