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Solved problems for the chapter:

Time Measurement, Units and Measuring Devices

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Unit conversion

1. Meaning of unit conversion

2. SI prefixes

3. Forum

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Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:time_measurement%2C_units_and_measuring_devices/3504/

Example 1.

Five sports cars A, B, C, D, and E compete in a race. The table below shows the finishing times for the cars.

Cars	A	B	C	D	E
Finishing time ()	32.60	29.80	31.50	33.10	30.00

Which of the statements below is correct?

Car B won the race and was ahead of the car in second place.
Car B won the race and was ahead of the car in second place.
Car D came last and was behind the car in first place.
Car D came last and was behind the car in first place.

Example 2.

The figure below shows the times on the stopwatch at the start and at the end of a run by an athlete in a race.

How long did the athlete take to run the race?

The total time taken to make 50 complete swings by a pendulum is shown below.

What is the time period for 1 complete swing?

A student uses a stopwatch to measure the time for a car to make 5 laps of the track in a car race around a track. The student forgets to reset the stopwatch at the start of the race. The figure below shows the time on the stopwatch at the start and the time after going around the track 5 times at a constant rate.

Calculate, in seconds, the time it takes the car to go around the track once.

Five students P, Q, R, S, and T each measure the time taken for a pendulum to make 10 complete swings. The results of their measurements are shown in the table below.

Students	P	Q	R	S	T
Measurements ()	20.9	21.0	21.2	21.2	21.2

What is the average period of the pendulum?

The figure below shows the length of a candle at the start and end of an experiment carried out by a boy using a burning candle.

How long did the candle burn?

The figure below shows a pendulum bob which swings from point A to B.

A student starts a stop-watch when the bob reaches point A. He counts each time the bob changes direction and stops the watch on the twentieth change in direction. If the watch shows a time of 15.0 seconds, what is the period of the pendulum?

A cyclist rides round a circular track six times. Using a stopwatch, his colleague records the times at the start of the ride, after one circuit, and at the end of the six circuits. The readings on the stopwatch are shown below.

What is the average time for one circuit of the track?

Four students W, X, Y and Z try to measure the time period (the time for one complete oscillation) of a pendulum. The arrows in the figure below show the movements of the pendulum that each student measures its time period.

Which student has chosen the correct movement for one period of a pendulum?

10.

Three students each use a digital stopwatch to time a small trolley rolling down the full length of a slope. The times on their stopwatches, as the trolley reached the bottom of the slope, are shown below.

Calculate the average time measured for the trolley to roll down the full length of the slope.

11.

The blades on a wind turbine are turning slowly, so a student uses a laboratory stopclock to time 40 rotations of the blades. The stopclock after 40 rotations is shown below.

Calculate, in seconds, the time for one rotation of the blades.

12.

Some students measure the time taken for 50 drops to fall from the tap shown below.

If the time measured by the students for 50 drops is , calculate the average time between two drops falling.

13.

The figure below shows the time taken for 50 periods of a pendulum.

Calculate the time for one period of the pendulum. Give your answer to 2 decimal places.

14.

A tap fills a container with drops. A student uses a stop-watch to measure the time taken for the tap to produce 250 drops. The figure below shows the time reading on the stop-watch.

What is the time in seconds?

15.

The figure below shows the times recorded on the stopwatches for the winner and the swimmer in second place in a swimming competition.

What is the time for the winner?
What is the time difference between the winner and the swimmer in second place?

16.

The figure below shows the stopwatch readings at the start and end of an experiment carried out by a student.

Calculate, in seconds, the time interval between the two readings.

17.

A student analyses the motion of a train. He starts a digital timer as the train starts to move and records the time that the train enters station A and the time it enters station B as shown below.

Calculate, in seconds, the time taken from the train entering station A to the train entering station B.

18.

A student collects water from a tap with a bowl. He uses a digital stopwatch to measure the time between when two drops of water hit the bowl. He repeats his measurements and the results are shown below.

Calculate the average time between two drops of water.
Using the result in (a) above, calculate how many drops leave the tap if the student collects drops of water for 6.2 minutes.

19.

A gardener must collect water from a tap into an empty tank, which must be filled by 1.15 p.m. He uses a tap with an automatic timer which can be set to switch on and off at certain times. The tap needs to be switched on for 3 hours 40 minutes in order to fill up the empty tank. At what time of the day does the tank need to switch on?

20.

Two boys, P and Q, stand at a distance apart on a straight road and decide to measure the time taken by a van, traveling at a constant speed, to move from boy P to boy Q.

Boy Q has a stopwatch which he sets to zero. As the van passes boy P, boy P drops his hand as a signal to boy Q to start his stopwatch. Boy Q then stops the stopwatch as the van goes past him. The appearance of the stopwatch at the end is shown below.

How long did it take for the van to travel from boy P to boy Q?

21.

Convert and appropriately express the result in a scientific notation.

22.

Converts from minutes to milliseconds and appropriately express the result in a scientific notation.

23.

Convert:

24.

Convert:

25.

Convert and express the result in a scientific notation.

26.

Convert and express the result in a scientific notation.

27.

Convert:

28.

Convert and appropriately express the results in a scientific notation.

29.

Convert and appropriately express the result in a scientific notation.

30.

Convert and express in a scientific notation.

31.

Convert and appropriately express the result in a scientific notation.

32.

Convert to the appropriate unit using a scientific notation.

33.

Convert and round the result to two decimal places:

34.

Convert and round the result to two decimal places:

35.

Convert and express the result in a scientific notation.

36.

Convert and appropriately express the result in a scientific notation.

37.

Convert and appropriately express the result in a scientific notation.

38.

Convert and express the result in a scientific notation.

39.

Convert and round to one decimal place:

40.

Convert and appropriately express the result in a scientific notation.

41.

Convert and write the solution in a standard form in exactly 3 significant figures.

42.

A boy's clock is 2 seconds behind every 3 hours. By how many minutes is the clock behind in 30 days?

43.

One light-year is the distance light travels in one year. The light travels through the Earth and reaches a distance of every second. Calculate how many meters a light-year measures. Note that a year equals 365.25 days.

44.

A train departs from the capital towards the northern city at exactly 5:40 am. At what time does it reach its destination if the ride takes ?