Motion in a Straight Line - Quick Revision
Basics
- Position relative to a chosen origin (+/-). Path length (scalar) >= |displacement| (vector).
- Average velocity = Δx/Δt; average speed = path length/Δt >= |average velocity|.
- Instantaneous v = dx/dt (slope of x-t), a = dv/dt (slope of v-t). Instantaneous speed = |instantaneous velocity|.
Acceleration
- a = Δv/Δt. May arise from change in speed, direction, or both.
- Sign of a alone doesn't tell if speeding up/down (depends on chosen +direction). Speeding up: a along v; slowing: a opposite v.
- v=0 at an instant does NOT mean a=0 (ball at top of throw: a=g).
Graphs
- x-t: rest -> line parallel to t-axis; uniform motion -> inclined line; uniform acceleration -> parabola.
- v-t: slope = a; area under v-t = displacement.
Equations (uniform acceleration only)
- v = u + at; x = ut + ½at²; v² = u² + 2ax; s_n = u + (a/2)(2n-1).
- Free fall: v = gt, h = ½gt² (a = -g if up positive). Vertical throw: H = u²/2g, t_up = u/g, T = 2u/g.
- Galileo's odd-number law: distances in equal successive intervals 1:3:5:7...
- Relative velocity (1-D): v_AB = v_A - v_B; stopping distance d = u²/2a (proportional to u²).