← all cardsTopic 10 · Oscillations · State of motion & graphs
Reading directions off an x–t graph
At any point: v = sign of the gradient; a = opposite sign of x (always towards centre). So: moving away from equilibrium → v and a opposite (slowing down); moving towards equilibrium → v and a same direction (speeding up). That's the whole "at which point are v and a opposite" MCQ.
What this actually means
At any instant on an x–t graph: velocity is the sign of the gradient, and acceleration takes the opposite sign of x, because it always aims at the centre.
Put together: moving away from equilibrium, v and a oppose each other (the mass is decelerating); moving towards it, they agree (speeding up).
That single pairing rule is the entire 'at which point are v and a in opposite directions' multiple-choice question.
Prove it — watch it be true
- Put the tangent on the x–t graph while the curve is climbing away from equilibrium: positive gradient, so v is positive
- Read a–t at that same instant: a carries the opposite sign to x, so v and a oppose and the mass is slowing down
- Move the tangent to a point heading back towards equilibrium: v and a now share a sign and the mass speeds up — that pairing is the whole MCQ