Units, Time and Conversions ഭൗതിക അളവ്
Every answer in this chapter is a number with a unit: 50 s, 20 m/s, 2 m/s². Many questions give speeds in km/h, times in minutes and lengths in cm. You must change these into metres and seconds before you use a formula. This page explains the units of motion, what “per second” really means, and how to change km/h into m/s and back.
- Multiplying and dividing by 10, 100, 1000 and 60.
- Simple fractions such as 5/18 (also revised on page 4).
1. Physical quantities and their SI units
Anything that can be measured and written as a number × a unit is a physical quantity (ഭൗതിക അളവ്). Scientists all over the world use the same set of units, the SI units. For motion we need only metres and seconds, and the units built from them:
| Physical quantity | Symbol | SI unit | Read it as |
|---|---|---|---|
| distance (ദൂരം), displacement (സ്ഥാനാന്തരം) | s | m | metre |
| time | t | s | second |
| speed (വേഗം), velocity (പ്രവേഗം) | v (and u) | m/s | metre per second |
| acceleration (ത്വരണം) | a | m/s² | metre per second squared |
Always write the unit with the number, with a space between them: 20 m/s, not “20” or “20m/s”. Don't mix up the symbol s (displacement) with the unit s (second): “s = 120 m” means a displacement of 120 metres, but “t = 120 s” means a time of 120 seconds.
2. Bigger and smaller units
Long distances are measured in kilometres (km) and short ones in centimetres (cm) or millimetres (mm). Long times are in minutes (min) or hours (h). Before using any formula of motion, change them into metres and seconds.
| Length | Time |
|---|---|
| 1 km = 1000 m | 1 min = 60 s |
| 1 m = 100 cm = 1000 mm | 1 h = 60 min = 60 × 60 s = 3600 s |
| 1 cm = 1/100 m = 0.01 m | ½ h = 30 min = 1800 s |
| 1 mm = 1/1000 m = 0.001 m | 10 min = 600 s |
Going down the ladder (to a smaller unit) you multiply: there are more of the small units. Going up (to a bigger unit) you divide. The green box is the SI unit you need for the formulas.
A smaller unit always needs a bigger number: 2 km = 2000 m (more metres than kilometres). A bigger unit needs a smaller number: 2 cm = 0.02 m. If your conversion goes the other way, you have multiplied where you should have divided.
3. What “per second” means
“Per” means “for each” or “in every”. A speed of 20 m/s (20 metres per second) means the object covers 20 metres in every second. So in 6 seconds it covers 20 + 20 + 20 + 20 + 20 + 20 = 20 × 6 = 120 m. That is why
The blue dots show where the bus was after 1 s, 2 s, 3 s … The gaps are all equal, because the bus moves the same number of metres in every second.
The unit of acceleration: m/s²
Acceleration tells how much the velocity changes in every second. If a bus's velocity goes 0 → 3 → 6 → 9 m/s, second after second, its velocity grows by 3 m/s in every second. We write this as 3 (m/s) per second = 3 m/s ÷ s = 3 m/s². The “²” appears because “per second” is used twice: metres per second, per second.
Each bar is the velocity at the end of a second. Each bar is taller than the one before by exactly a, the acceleration.
4. Changing km/h into m/s, and back
Speedometers and road signs in Kerala show speeds in km/h (kilometres per hour), but the formulas need m/s. Here is where the magic fraction 5/18 comes from:
(1000/3600: divide the top and the bottom by 200 to get 5/18.) So:
km/h → m/s: multiply by 5/18. 90 km/h = 90 × 5/18 = 25 m/s.
m/s → km/h: multiply by 18/5. 25 m/s = 25 × 18/5 = 90 km/h.
Memory aid: m/s numbers are always smaller than the km/h numbers for the same speed, because 5/18 is less than 1.
Outer numbers: km/h (as on a speedometer). Inner purple numbers: the same speeds in m/s. Every 18 km/h is exactly 5 m/s. The blue bar on the right shows how many metres the vehicle covers in one second.
| km/h | 18 | 36 | 54 | 72 | 90 | 108 | 144 |
|---|---|---|---|---|---|---|---|
| m/s | 5 | 10 | 15 | 20 | 25 | 30 | 40 |
When a Kochi Metro train cruises at 72 km/h, it covers 20 metres every second. An autorickshaw at 36 km/h covers 10 m every second. If the driver looks at a phone for just 2 seconds, the autorickshaw travels 20 m “blind”. That is longer than a zebra crossing is wide! Thinking in m/s shows why road safety rules matter.
Worked example 1 · km/h into m/s
Q. A train reaches a speed of 90 km/h. Express this speed in m/s.
km/h → m/s: multiply by 5/18. Simplify 90/18 first: 90 ÷ 18 = 5.
Worked example 2 · Both quantities into SI units
Q. A train starting from rest reaches 72 km/h in 5 minutes. Write its final velocity in m/s and the time in seconds.
Velocity: × 5/18. Time: 1 min = 60 s, so × 60.
Worked example 3 · m/s into km/h
Q. A KSRTC bus moves at 15 m/s on a straight road. What does its speedometer show, in km/h?
m/s → km/h: multiply by 18/5. 15 ÷ 5 = 3 first.
Putting km/h or minutes straight into v = u + at or s = ut + ½at² gives a wrong answer. Convert first, then substitute. A train that reaches 90 km/h in 10 minutes has v = 25 m/s and t = 600 s, not 90 and 10.