Describing Motion Around Us
Speed and velocity
Find out how speed and velocity differ.
Start with what you know. At the vegetable stall you ask, 'What is the rate?' The seller says '₹40 per kg'. 'Rate' and 'per' mean divided by. In motion, a rate is something divided by time.
Speed: how fast. Average speed = total distance ÷ total time.
Example: you cycle 100 m in 20 s. Average speed = 100 ÷ 20 = 5 m per second. Speed tells you how fast, but not which way.
The units. Speed is measured in metres per second, written m/s or m s⁻¹. On roads we also use kilometres per hour (km/h, or km h⁻¹).
Steady or not?
- Uniform motion: equal distances in equal times. The speed stays the same, like a train on a long straight track.
- Non-uniform motion: unequal distances in equal times. The object speeds up, slows down, or both, like a bus in city traffic.
India knew this long ago. The idea of speed as distance ÷ time appears in the Aryabhatiya (5th century CE). The Ganitakaumudi (14th century CE) asks a puzzle: two postmen are 210 yojanas apart and walk towards each other at 9 and 5 yojanas a day. When do they meet? Together they close 9 + 5 = 14 yojanas a day, so they meet after 210 ÷ 14 = 15 days.
Velocity: how fast, and which way. Velocity is speed with a direction attached.
Average velocity = displacement ÷ total time, written v_av = s/t. Here s is the displacement and t the time. Its direction is the direction of the displacement (+ or – on a line).
Sarang in the pool. He swims 25 m to the end and 25 m back, in 50 s.
- Average speed = distance ÷ time = 50 m ÷ 50 s = 1 m s⁻¹.
- Average velocity = displacement ÷ time = 0 m ÷ 50 s = 0 m s⁻¹, because he ended where he began.
He was clearly moving, yet his average velocity is zero. That is the difference between the two.
When are they the same? Speed and velocity have the same size only when the motion is in one direction, with no turning back.
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