Measurement of Time and Motion: questions with answers

A sundial shows local solar time, based on the Sun's position at that place. Its finely marked scale does not make it show Indian Standard Time. A correction is needed to obtain Indian Standard Time.

A pendulum clock counts the swings of its pendulum. An atomic clock counts a movement that repeats inside atoms. Both clocks count a process that repeats continuously, so the basic principle is the same. The atomic clock keeps better time because its repeating process is far faster and far more even.

The flowing-out water clock was not very accurate, because as the water level dropped the flow rate decreased. That is what led to the sinking bowl water clock, the Ghatika-yantra. Its bowl was made to take 24 minutes to fill and sink, dividing a 24-hour day into 60 equal ghatis.

One complete oscillation is one full to-and-fro motion. Starting at O towards A, the complete path is O to A to B and back to O. Starting at A, it is A to B and back to A. The path from O to A represents part of an oscillation.

Galileo timed a swinging lamp against his own pulse. He found that each swing took the same time. The time period of a simple pendulum of a given length is constant at a place. It does not depend on the weight of the bob. Since every swing takes the same time, counting the swings measures time in a clock.

The time period of a simple pendulum depends on its length but not on the mass of its bob. Changing the length changes the time period; changing the bob for a heavier or a lighter one of the same size leaves the time period as it was.

There are 60 min in 1 h, so going from minutes to the larger unit divides by 60. Multiplying instead makes the number larger, which cannot be right: an hour is longer than a minute, so the same interval must be a SMALLER number of hours.

The SI unit of time is the second. Since 1 min = 60 s, 90 min = 90 × 60 s = 5400 s. An answer in minutes is not in the SI unit. Multiply by 60, not 100, and change the number as well as the unit.

The symbols for time are s for second, min for minute and h for hour. They are written in lowercase and in the singular. A space is always left between the number and the unit. Writing sec for second or hrs for hour is incorrect.

Speed is the distance covered in a unit of time. Divide each total distance by the time taken, and express both speeds in the same unit. The greater speed tells you which moved faster.

Over the same distance, the runner who takes less time is faster. Meera takes the shorter time of 12 s, so Meera ran faster.

Average speed = total distance ÷ total time. It describes the whole journey, even when the speed changes. Adding the separate speeds and dividing by their number does not generally give the average speed.

Speed is the total distance covered divided by the total time taken, so the distance in metres is divided by the time in seconds. Because the distance comes first in that division, the unit is metre/second, written m/s.

Both trains cover 120 km in 1 hour, giving the same average speed of 120 km/h. Using the equal-time intervals given, X covers equal distances (20 km each), while Y covers unequal distances. Under the school interval-based classification on straight tracks, X is uniform and Y is non-uniform.

Uniform linear motion is an idealisation, and in everyday life objects seldom move at a constant speed. That is why average speed is used. The total distance divided by the total time gives one speed for the whole journey, even though the speed kept changing.