Calculus · Maths AA SL
Velocity & displacement
Displacement describes position relative to a chosen origin. Velocity describes how quickly that displacement changes.
v(t) = dsdt
Three questions to ask
Is it at rest? Solve v(t) = 0. This gives candidate stationary times, not necessarily a change of direction.
Which direction? Positive velocity indicates the positive direction; negative velocity indicates the negative direction.
Where is it? Substitute the time into s(t), not v(t).
Check the intervals
Use a sign chart or suitable test values between consecutive roots. Keep your conclusion within the time domain in the question.