← all cardsTopic 8 · 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
- Pause the motion while the mass climbs away from equilibrium
- Gradient positive so v positive; x positive so a negative: opposed, slowing
- Pause on the way back: v and a now share a sign, and the mass speeds up