Speed Distance TimeSpeed Distance Time

Mastery of the core relationship among speed, distance, and time forms the bedrock of solving all advanced problems in this domain.

• Basic Formula Relationship: Distance = Speed × Time (d = s × t). Consequently, Speed = Distance / Time and Time = Distance / Speed.
• Kilometer per Hour to Meter per Second Conversion: To convert km/h to m/s, multiply the given value by 5/18. For instance, 90 km/h = 90 × (5/18) = 25 m/s.
• Meter per Second to Kilometer per Hour Conversion: To convert m/s to km/h, multiply the given value by 18/5. For instance, 20 m/s = 20 × (18/5) = 72 km/h.
• Proportionality Principle: When distance is constant, speed is inversely proportional to time (s ∝ 1/t). If speed increases in the ratio a:b, time taken decreases in the ratio b:a.
• Average Speed for Equal Distances: If a body covers a distance at speed 'x' and an equal distance at speed 'y', the average speed is given by 2xy / (x + y).

Exam questions frequently feature moving objects interacting with each other or with external mediums like flowing water.

• Objects Moving in Opposite Directions: If two bodies move towards each other with speeds 'u' and 'v', their relative speed is (u + v).
• Objects Moving in the Same Direction: If two bodies move in the same direction with speeds 'u' and 'v' (where u > v), their relative speed is (u - v).
• Crossing a Pole or Stationary Point: When a train of length 'L' crosses a pole, man, or tree, the distance covered is equal to the length of the train itself (Time = L / Speed).
• Crossing a Platform or Bridge: When a train of length 'L1' crosses a platform of length 'L2', the total distance to cover is (L1 + L2).
• Boats and Streams: Downstream and Upstream: Let boat speed in still water be 'b' and stream speed be 's'. Downstream Speed = b + s; Upstream Speed = b - s.
• Calculating Still Water and Stream Speeds: If downstream speed is 'D' and upstream speed is 'U', then Boat speed in still water = (D + U) / 2 and Stream speed = (D - U) / 2.

Advanced problem types test simultaneous starts, meeting points on circular tracks, and variable speed scenarios.

• Meeting on a Circular Track (Same Direction): If two runners with speeds 'u' and 'v' (u > v) run on a circular track of length 'C' in the same direction, time taken to meet for the first time is C / (u - v).
• Meeting on a Circular Track (Opposite Directions): If two runners with speeds 'u' and 'v' run in opposite directions on a track of length 'C', time taken to meet for the first time is C / (u + v).
• Stoppages and Net Speed: Excluding stoppages, if a bus travels at speed 'S1' and including stoppages at speed 'S2', then stoppage time per hour = [(S1 - S2) / S1] × 60 minutes.
• Variable Speeds and Time Differences: If a person covers a distance at two different speeds 's1' and 's2', resulting in a time difference 'T', the distance is calculated as: D = [s1 × s2 / (s1 ~ s2)] × T.