Time, Speed & Distance
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Speed, Distance, Time & Unit Conversion
Basic relation
S = \frac{D}{T}, \quad D = S \times T
km/h to m/s
\text{km/h} \times \frac{5}{18} = \text{m/s}
Equal-distance average
\bar{S} = \frac{2ab}{a + b}
General average speed
\bar{S} = \frac{D_1 + D_2}{T_1 + T_2}
Relative Speed
Relative speed
S_{rel} = S_1 \pm S_2
Meeting time
t = \frac{\text{initial gap}}{S_1 + S_2}
Overtake time
t = \frac{\text{gap or combined length}}{S_1 - S_2}
Gap between two movers
d = (S_1 \pm S_2) \times t
Trains Crossing Poles, Platforms & Trains
Pole / man
L_{train} = S \times t
Platform / bridge
L_{train} + L_{platform} = S \times t
Train vs train
L_1 + L_2 = S_{rel} \times t
Two-equation extraction
S = \frac{P}{t_{platform} - t_{pole}}
Boats & Streams
Effective speeds
u = b + s, \quad v = b - s
Boat and stream from legs
b = \frac{u + v}{2}, \quad s = \frac{u - v}{2}
Time for two legs
t = \frac{d_1}{b + s} + \frac{d_2}{b - s}
Round-trip average
\bar{S} = \frac{2uv}{u+v} = \frac{b^2 - s^2}{b}
Drift
\text{drift} = s \times \text{time}
Races & Handicaps
Beating margin in metres
\frac{S_A}{S_B} = \frac{D}{D - x}
Beating margin in time
t_B = t_A + t; \quad S_B = \frac{x}{t}
Start handicap
B \text{ runs } D - \text{start} \ ( - \text{win margin})
Circular track meeting
t = \frac{L}{S_1 \mp S_2}