Revise: Motion

Scalars: size only. Vectors: size AND direction.

6 m/s east + 2 m/s west → 4 m/s east.

Distance = total path length. Displacement = straight-line, with direction.

One lap of a track: distance 400 m, displacement 0 m.

speed = distance / time

150 m in 30 s → 5 m/s.

a = (v − u) / t

10→30 m/s in 5 s → 4 m/s².

v = u + at

u=5, a=3, t=4 → v=17 m/s.

g ≈ 9.8 m/s² for every object near Earth.

Dropped for 2 s → falls 19.6 m.

Vectors are drawn as arrows; along one line they add like signed numbers.

15 N right, 9 N left → resultant 6 N right.

Distance (scalar) vs. displacement (vector, net change).

300 m east then 100 m west → distance 400 m, displacement 200 m east.

speed = distance / time (scalar).

100 m in 20 s → 5 m/s.

velocity = displacement / time (vector, has direction).

40 m north in 8 s → 5 m/s north.

Slope of a distance-time graph = speed.

(0,0) to (5,20) → speed 4 m/s.

a = (v−u)/t — deceleration is negative acceleration.

12→0 m/s in 4 s → −3 m/s².

Slope of a velocity-time graph = acceleration; area under it = displacement.

(0,5) to (10,25) → acceleration 2 m/s².

v = u + at — final velocity from initial, acceleration, time.

u=5, a=3, t=4 → v=17 m/s.

s = ut + ½at² — displacement without needing final velocity.

u=2, a=4, t=3 → s=24 m.

v² = u² + 2as — use when time is unknown.

u=4, a=2, s=24 → v≈10.6 m/s.

Free fall is uniform acceleration under gravity — substitute g for a.

Dropped for 3 s → v = 29.4 m/s.