Measurement and Motion
Measurement and Motion is the foundation domain of the Madhyamik Physical Science paper: it checks whether you can choose SI units, read laboratory instruments correctly and describe motion with equations and graphs rather than vague words.
Measurement rules
- SI base units used here are metre (length), kilogram (mass) and second (time); derived units include newton (force), joule (work) and watt (power).
- Least count of a vernier caliper is 1 main-scale division minus 1 vernier-scale division. For a screw gauge it is pitch divided by the number of circular-scale divisions.
- Record a measurement to the precision of the instrument and convert cm to m before substituting in formulae.
Motion rules
- Distance is scalar; displacement is vector. Speed is distance/time; velocity is displacement/time; acceleration is change in velocity/time.
- For uniform acceleration: v = u + at, s = ut + 1/2at^2, v^2 = u^2 + 2as.
Worked example
A car speeds up uniformly from 10 m/s to 20 m/s in 5 s. Find acceleration and distance. a = (20 - 10)/5 = 2 m/s^2. Then s = 10(5) + 1/2(2)(5^2) = 50 + 25 = 75 m. Check: v^2 = u^2 + 2as gives 400 = 100 + 4s, so s = 75 m.
Traps
- Subtracting final and initial positions without sign gives displacement errors.
- Using speed and velocity as synonyms in numerical answers.
- Forgetting zero-error correction on vernier and screw-gauge readings.
- Mixing km/h with m/s; convert by dividing by 3.6.