Measurement of Time and Motion
Learn how time is measured, investigate the motion of a simple pendulum, calculate speed, and distinguish between uniform and non-uniform linear motion.
Chapter Snapshot
- Regularly repeating events have been used to measure time since ancient times.
- The SI unit of time is the second, written as s.
- Clocks, watches and stopwatches provide convenient ways of measuring time.
- A simple pendulum consists of a small bob suspended from a fixed support by a light string.
- One complete to-and-fro motion of a pendulum is called an oscillation.
- The time required for one complete oscillation is called the time period.
- An object is in motion when its position changes with time relative to a reference point.
- Speed tells us how much distance an object travels per unit time.
- The SI unit of speed is metre per second, written as m/s.
- In uniform linear motion, equal distances are covered in equal intervals of time.
- In non-uniform linear motion, unequal distances are covered in equal intervals of time.
What You Will Learn
- Explain why measurement of time is important in everyday life
- Describe traditional and modern methods of measuring time
- State the SI unit of time and convert between common time units
- Identify the main parts of a simple pendulum
- Define oscillation and time period of a pendulum
- Measure the time period of a simple pendulum experimentally
- Explain motion using the idea of a reference point
- Compare the speeds of moving objects
- Calculate speed using distance and time
- Calculate distance or time when other quantities are known
- Distinguish between uniform and non-uniform linear motion
- Interpret simple motion tables and distance-time representations
Chapter Overview
Imagine watching a 100-metre race.
Two runners cross the finish line almost together. How can we decide who won?
We need to measure the time taken by each runner accurately.
Now imagine two vehicles travelling on a road. One covers a much greater distance than the other in the same amount of time.
How can we compare how fast they are moving?
We need the concept of speed.
Measurement makes words such as "quick", "slow", "long time" and "short time" scientifically meaningful.
This chapter connects two important ideas:
- measurement of time;
- description of motion.
Detailed Explanation
1. Why Do We Need to Measure Time?
We use time measurement throughout the day.
Examples include:
- waking up for school;
- timing a race;
- knowing the duration of a class;
- planning a journey;
- cooking food;
- measuring a scientific experiment;
- scheduling trains and flights;
- comparing sporting performances.
Without standard measurement, one person's idea of a "short time" may be very different from another person's.
Scientific measurement therefore requires:
- a standard unit;
- a reliable measuring device;
- careful observation.
2. How Did People Measure Time in the Past?
Modern watches and clocks were not always available.
People observed natural events that repeated regularly.
Examples include:
- sunrise and sunset;
- phases of the Moon;
- seasonal changes;
- movement of shadows.
These repeating patterns helped people estimate longer periods of time.
Natural measures of time
A day is related to the rotation of the Earth.
A year is related to the revolution of the Earth around the Sun.
Months were historically connected with repeating changes in the appearance of the Moon.
Natural events, however, are not convenient for measuring short intervals such as:
- a few seconds;
- the duration of a race;
- the time taken for an experiment.
People therefore developed different time-measuring devices.
3. Traditional Time-Measuring Devices
Sundial
A sundial uses the changing position of a shadow produced by sunlight.
A major limitation is that it requires suitable sunlight.
Water Clock
Water clocks were designed so that water flowed at a controlled rate.
The amount of water collected or lost could be used to estimate elapsed time.
Sand Clock
A sand clock, or hourglass, contains two chambers joined by a narrow opening.
Sand flows gradually from one chamber to the other.
These traditional devices demonstrate an important principle:
A regularly repeating or sufficiently steady process can be used to measure time.
4. Modern Measurement of Time
Today we commonly use:
- wall clocks;
- wristwatches;
- digital clocks;
- mobile phones;
- stopwatches;
- electronic timers.
A stopwatch is especially useful for measuring short time intervals.
Modern sporting competitions may use electronic timing because even a fraction of a second can affect the result.
Use an ordinary clock for general timekeeping.
Use a stopwatch or timer when measuring short experimental or sporting time intervals.
5. Units of Time
Scientific measurements require standard units.
Common larger units are:
- minute;
- hour;
- day.
Time Conversions
Therefore:
and:
We know:
Therefore:
Thus:
We know:
Therefore:
Thus:
Show answer
6. Periodic Motion
A movement that repeats itself after equal intervals of time can be useful for measuring time.
One important example is a swinging pendulum.
Examples include:
- repeated oscillation of a pendulum under suitable conditions;
- regular vibration of certain objects;
- repetitive motion used in some clocks.
7. The Simple Pendulum
A simple pendulum can be made using:
- a small heavy object called a bob;
- a light string;
- a fixed support.
Mean Position
When the pendulum hangs freely at rest, the bob occupies its central position.
This is called the mean position.
Extreme Positions
When the bob swings, it reaches the farthest point on each side before reversing direction.
These are called the extreme positions.
Suppose:
- O = mean position;
- A = one extreme position;
- B = the other extreme position.
One complete to-and-fro motion can be represented as:
8. Time Period of a Pendulum
The time taken by a pendulum to complete one oscillation is called its time period.
If the total time for several oscillations is measured, the time period can be calculated.
Time Period of a Pendulum
where:
- T = time period of one oscillation;
- t = total measured time;
- N = number of complete oscillations.
The SI unit of time period is the second (s).
Given
Formula
Substitution
Calculation
Therefore:
Show answer
9. What Is Motion?
We see motion everywhere:
- birds fly;
- cars move;
- people walk;
- a ball rolls;
- leaves fall;
- trains move along tracks;
- planets move around the Sun.
But what exactly do we mean by motion?
The phrase reference point is important.
A student sitting inside a moving bus is:
- at rest relative to the seat;
- moving relative to a tree beside the road.
Thus, motion must be described relative to something.
10. Linear Motion
An object moving along a straight path shows linear motion.
Examples include:
- a car travelling along a straight road;
- a sprinter running on a straight track;
- a lift moving vertically;
- an object falling vertically.
11. Slow and Fast Motion
Suppose two students cover the same distance.
Student A takes 20 seconds.
Student B takes 15 seconds.
Student B is faster because the same distance was covered in less time.
Now suppose both move for 10 seconds.
Student A covers 40 metres.
Student B covers 60 metres.
Student B is again faster because a greater distance was covered in the same time.
This leads to the idea of speed.
12. Speed
Speed Formula
Using symbols:
where:
- v = speed;
- d = distance travelled;
- t = time taken.
SI Unit of Speed
The SI unit of distance is metre.
The SI unit of time is second.
Therefore:
Hence:
It may also be written as:
13. Calculating Speed
Given
Formula
Substitution
Calculation
Therefore:
Given
Formula
Substitution
Calculation
Therefore:
Show answer
14. Calculating Distance
The speed formula can be rearranged to find distance.
From:
we obtain:
Distance Formula
where:
- d = distance;
- v = speed;
- t = time.
Given
Formula
Substitution
Calculation
Therefore:
15. Calculating Time
From the speed formula:
time can be calculated using:
Time Formula
where:
- t = time;
- d = distance;
- v = speed.
Given
Formula
Substitution
Calculation
Therefore:
16. Common Units of Speed
Speed may be expressed in:
- metres per second;
- kilometres per hour.
For scientific calculations, the SI unit is:
A vehicle's speedometer commonly displays:
Speedometer vs Odometer
| Feature | Speedometer | Odometer |
|---|---|---|
| Measures | Speed | Distance travelled |
| Common unit | km/h | km |
| Purpose | Shows how fast a vehicle is moving | Records how far a vehicle has travelled |
17. Comparing Speeds Correctly
Suppose:
- Car A covers 100 km in 2 h;
- Car B covers 150 km in 3 h.
We should not decide that Car B is faster merely because it travelled farther.
Car A
Car B
Therefore:
Both have the same average speed over the journeys.
18. Uniform Linear Motion
Suppose a toy car covers:
- 5 m during the first second;
- 5 m during the second second;
- 5 m during the third second;
- 5 m during the fourth second.
It covers equal distances in equal intervals of time.
Example:
| Time Interval | Distance Covered | | ------------- | ---------------: | | 0–1 s | 5 m | | 1–2 s | 5 m | | 2–3 s | 5 m | | 3–4 s | 5 m |
Its speed remains constant.
19. Non-uniform Linear Motion
Consider a car moving through traffic.
During successive 10-second intervals it may travel:
- 80 m;
- 50 m;
- 20 m;
- 70 m.
The distances are different even though the time intervals are equal.
Its speed changes during the motion.
Examples include:
- a bus moving through traffic;
- a bicycle starting from rest and speeding up;
- a vehicle slowing near a traffic signal;
- a runner changing pace.
Uniform vs Non-uniform Linear Motion
| Feature | Uniform Linear Motion | Non-uniform Linear Motion |
|---|---|---|
| Path | Straight line | Straight line |
| Equal time intervals | Equal distances are covered | Unequal distances are covered |
| Speed | Constant | Changes |
| Example | Object moving steadily along a straight path | Vehicle speeding up or slowing down |
Show answer
20. Average Speed
Most real journeys are not perfectly uniform.
A bus may:
- start slowly;
- speed up;
- stop at a bus stop;
- slow near a junction;
- travel faster on an open road.
For the complete journey, we can calculate average speed.
Average Speed
Given
Formula
Substitution
Calculation
Therefore:
This does not mean that the bus moved at exactly 40 km/h at every moment.
21. Measuring Motion Experimentally
22. Reading Motion Data
Consider the following table.
| Time | Total Distance | | ---: | -------------: | | 0 s | 0 m | | 1 s | 4 m | | 2 s | 8 m | | 3 s | 12 m | | 4 s | 16 m |
During every one-second interval, the object covers 4 m.
Its speed is:
The motion is uniform.
Now consider:
| Time | Total Distance | | ---: | -------------: | | 0 s | 0 m | | 1 s | 2 m | | 2 s | 5 m | | 3 s | 9 m | | 4 s | 14 m |
The distances covered during successive one-second intervals are:
- 2 m;
- 3 m;
- 4 m;
- 5 m.
These are unequal.
Therefore, the motion is non-uniform.
23. Distance-Time Representation
Motion information can also be represented graphically.
A distance-time graph commonly shows:
- time along the horizontal axis;
- distance along the vertical axis.
For uniform motion, distance increases by equal amounts during equal intervals of time.
This produces a straight rising line.
24. Everyday Applications of Speed
Speed is important in many situations.
Road Safety
A faster-moving vehicle generally requires a greater distance to stop safely.
Drivers therefore need:
- appropriate speed;
- sufficient distance from the vehicle ahead;
- attention to road conditions.
Sports
Speed measurements help compare:
- runners;
- swimmers;
- cyclists;
- racing vehicles.
Transport
Speed helps estimate:
- journey duration;
- arrival time;
- transport efficiency.
Science
Scientists measure the motion of:
- animals;
- machines;
- water;
- air;
- celestial bodies.
Safe motion depends on the situation.
On crowded roads, sharp turns, slippery surfaces or near schools, a lower speed may be much safer.
Science helps us measure speed. Responsible behaviour helps us choose an appropriate speed.
25. A Complete Motion Problem Strategy
When solving numerical questions involving motion, follow these steps.
Step 1 — Identify the known quantities
Look for:
- distance;
- time;
- speed.
Step 2 — Choose the correct formula
For speed:
For distance:
For time:
Step 3 — Check units
Make sure the units are compatible.
Step 4 — Substitute values
Insert the known values carefully.
Step 5 — Calculate
Show the mathematical step.
Step 6 — Write the final answer with unit
Given
Formula
Substitution
Calculation
Therefore:
26. Concept Map
Concept Map
Formula Revision
Formula / Key Relations
Speed
where:
- v = speed;
- d = distance travelled;
- t = time taken.
SI unit:
Distance
Use this relation when speed and time are known.
Time
Use this relation when distance and speed are known.
Time Period of a Pendulum
where:
- T = time period;
- t = total measured time;
- N = number of oscillations.
Basic Time Conversion
Average Speed
Exam Focus
Important Exam Areas
- importance of time measurement;
- traditional methods of measuring time;
- sundial, water clock and sand clock;
- modern clocks and stopwatches;
- SI unit of time;
- conversion of minutes, hours and seconds;
- periodic motion;
- simple pendulum;
- bob, mean position and extreme positions;
- meaning of one oscillation;
- time period of a pendulum;
- calculation of time period;
- definition of motion;
- importance of a reference point;
- linear motion;
- definition of speed;
- speed, distance and time calculations;
- SI unit of speed;
- speedometer and odometer;
- uniform linear motion;
- non-uniform linear motion;
- interpretation of motion tables;
- simple distance-time representations;
- average speed;
- applications of speed in everyday life.
Key Terms
Key Terms
Quick Revision
Quick Revision
- Time measurement is important in science, sports, transport and daily life.
- Early methods of measuring time used repeating natural events.
- Sundials use shadows produced by sunlight.
- Water clocks and sand clocks use controlled movement of materials.
- Modern clocks and stopwatches provide more convenient measurement.
- The SI unit of time is the second (s).
- One minute equals 60 seconds.
- One hour equals 60 minutes or 3600 seconds.
- Periodic motion repeats after equal intervals of time.
- A simple pendulum consists of a bob suspended by a string from a fixed support.
- One complete to-and-fro motion is one oscillation.
- The time taken for one complete oscillation is the time period.
- The time period can be found from total time divided by number of oscillations.
- Measuring several oscillations improves the reliability of pendulum timing.
- Motion means change of position with time relative to a reference point.
- Linear motion occurs along a straight path.
- Speed tells us the distance travelled per unit time.
- The SI unit of speed is metre per second.
- Distance can be calculated from speed multiplied by time.
- Time can be calculated from distance divided by speed.
- A speedometer measures speed.
- An odometer records distance travelled.
- Uniform linear motion covers equal distances in equal intervals of time.
- Non-uniform linear motion covers unequal distances in equal intervals of time.
- Average speed is total distance divided by total time.
- All numerical answers involving physical quantities should include appropriate units.
Practice Questions
A. Multiple Choice Questions
The SI unit of time is:
A. minute B. hour C. second D. day
View Solution
Correct Answer: C. second
The second, written as s, is the SI unit of time.
Which device is most suitable for timing a 100-metre race?
A. Ruler B. Stopwatch C. Odometer D. Thermometer
View Solution
Correct Answer: B. Stopwatch
A stopwatch is designed to measure short time intervals accurately.
The time taken by a pendulum to complete one oscillation is called:
A. speed B. distance C. time period D. path length
View Solution
Correct Answer: C. time period
The time period is the time required for one complete oscillation.
A pendulum completes 10 oscillations in 20 seconds. Its time period is:
A. 0.5 s B. 2 s C. 10 s D. 20 s
View Solution
Using:
we get:
Correct Answer: B. 2 s
Speed is equal to:
A. distance × time B. distance ÷ time C. time ÷ distance D. distance + time
View Solution
Correct Answer: B. distance ÷ time
A runner travels 80 m in 10 s. The speed is:
A. 8 m/s B. 80 m/s C. 800 m/s D. 0.8 m/s
View Solution
Correct Answer: A. 8 m/s
A vehicle covers equal distances in equal intervals of time along a straight road. Its motion is:
A. non-uniform linear motion B. uniform linear motion C. random motion D. oscillatory motion
View Solution
Correct Answer: B. uniform linear motion
Equal distances are covered in equal intervals of time.
Which instrument records the distance travelled by a vehicle?
A. Speedometer B. Odometer C. Stopwatch D. Sundial
View Solution
Correct Answer: B. Odometer
An odometer records the distance travelled by a vehicle.
B. Very Short Answer Questions
- What is the SI unit of time?
- Define one oscillation of a pendulum.
- What is the time period of a pendulum?
- Write the formula for speed.
- State the SI unit of speed.
- What does a speedometer measure?
- What does an odometer measure?
- Define linear motion.
- What is uniform linear motion?
- What is non-uniform linear motion?
Answers
-
Second, written as s.
-
One complete to-and-fro motion of a pendulum is one oscillation.
-
The time taken for one complete oscillation is called the time period.
-
Metre per second, written as m/s.
-
A speedometer measures speed.
-
An odometer records distance travelled.
-
Motion along a straight-line path is called linear motion.
-
Uniform linear motion occurs when equal distances are covered in equal intervals of time along a straight path.
-
Non-uniform linear motion occurs when unequal distances are covered in equal intervals of time along a straight path.
C. Short Answer Questions
Why is it better to measure the time for 20 oscillations of a pendulum rather than only one?
View Solution
Starting and stopping a stopwatch exactly introduces a small reaction-time error.
If only one oscillation is timed, this error can affect the result significantly.
If several oscillations are timed, the time period can be calculated using:
This reduces the relative effect of the timing error.
Distinguish between a speedometer and an odometer.
View Solution
A speedometer measures how fast a vehicle is moving.
An odometer records the total distance travelled by the vehicle.
Typical units are:
- speedometer → km/h;
- odometer → km.
Explain why motion must be described relative to a reference point.
View Solution
An object's position can be different relative to different surroundings.
For example, a passenger sitting in a moving bus is:
- at rest relative to the seat;
- moving relative to a roadside tree.
Therefore, whether an object is moving depends on the chosen reference point.
Differentiate between uniform and non-uniform linear motion.
View Solution
Uniform Linear Motion
The object moves along a straight path and covers equal distances in equal intervals of time.
Its speed remains constant.
Non-uniform Linear Motion
The object moves along a straight path but covers unequal distances in equal intervals of time.
Its speed changes.
D. Numerical Questions
A cyclist covers 300 metres in 60 seconds. Calculate the speed.
View Solution
Given
Formula
Substitution
Calculation
Therefore:
A car moves at 12 m/s for 25 seconds. Calculate the distance travelled.
View Solution
Given
Formula
Substitution
Calculation
Therefore:
A runner covers 400 metres at a speed of 8 m/s. Find the time taken.
View Solution
Given
Formula
Substitution
Calculation
Therefore:
A pendulum completes 25 oscillations in 50 seconds. Find its time period.
View Solution
Given
Formula
Substitution
Calculation
Therefore:
E. Application and HOTS Questions
Runner A covers 100 m in 20 s. Runner B covers 120 m in 24 s. Which runner is faster?
View Solution
Runner A
Runner B
Therefore:
Both runners have the same speed.
A bus travels 20 m during the first 5 seconds, 30 m during the next 5 seconds and 40 m during the next 5 seconds. Is its motion uniform? Explain.
View Solution
The time intervals are equal:
- 5 s;
- 5 s;
- 5 s.
But the distances are:
- 20 m;
- 30 m;
- 40 m.
These distances are unequal.
Therefore:
The bus is showing non-uniform motion.
Its speed is changing.
A passenger is sitting still inside a train moving at constant speed. Is the passenger at rest or in motion?
View Solution
The answer depends on the reference point.
Relative to the train seat, the passenger is at rest.
Relative to a person standing beside the railway track, the passenger is in motion.
Therefore, motion is relative to a chosen reference point.
Two cars travel for exactly 10 seconds. Car A covers 150 m and Car B covers 120 m. Which car is faster, and why?
View Solution
Car A
Car B
Since:
Car A is faster because it covers a greater distance in the same amount of time.
Why is recording the time for many pendulum oscillations scientifically better than recording only one oscillation?
View Solution
Human reaction time makes it difficult to start and stop a stopwatch at exactly the correct instant.
For one oscillation, even a small timing error can significantly affect the result.
When many oscillations are timed:
the effect of small timing errors is reduced.
Repeated trials can improve reliability further.
Assertion–Reason
Assertion: A faster object covers more distance than a slower object in the same amount of time.
Reason: Speed is distance travelled per unit time.
Choose the correct option:
A. Both Assertion and Reason are true, and Reason correctly explains Assertion. B. Both are true, but Reason does not explain Assertion. C. Assertion is true, but Reason is false. D. Both are false.
View Solution
Correct Answer: A
Speed tells us how much distance an object travels per unit time.
Therefore, for the same time interval, a faster object covers a greater distance.
Assertion: An object in uniform linear motion covers equal distances in equal intervals of time.
Reason: Its speed remains constant.
Choose the correct option:
A. Both Assertion and Reason are true, and Reason correctly explains Assertion. B. Both are true, but Reason does not explain Assertion. C. Assertion is true, but Reason is false. D. Both are false.
View Solution
Correct Answer: A
Constant speed means that equal distances are covered in equal time intervals.
Assertion: One complete oscillation of a pendulum is motion from one extreme position to the other extreme position only.
Reason: A complete oscillation requires the bob to return to its starting extreme position.
Choose the correct option:
A. Both are true. B. Assertion is true, but Reason is false. C. Assertion is false, but Reason is true. D. Both are false.
View Solution
Correct Answer: C
Moving from one extreme position to the other is only half of a complete oscillation.
The bob must return to the starting extreme position to complete one oscillation.
Apply Your Learning
Choose a safe straight path at school or home.
Mark a distance of 10 m.
Ask three participants to walk the same distance while another person measures their times.
Create a table:
| Participant | Distance | Time | Speed | | ----------- | -------: | ---: | ----: | | A | 10 m | ... | ... | | B | 10 m | ... | ... | | C | 10 m | ... | ... |
For each participant, calculate speed using:
Since the distance is 10 m:
Then answer:
- Who had the greatest speed?
- Who took the least time?
- When everyone covers the same distance, does the fastest participant take the least time?
- Why should each measurement be repeated?
- What factors could cause measurement error?
Common Mistakes to Avoid
Final Chapter Summary
Chapter Summary
- Accurate measurement of time is important in science, sports, transport and everyday life.
- Natural cycles and devices such as sundials, water clocks and sand clocks were used historically to measure time.
- Modern clocks and stopwatches provide convenient measurement of time intervals.
- The SI unit of time is the second (s).
- A simple pendulum consists of a bob suspended from a fixed support by a string.
- One complete to-and-fro motion of a pendulum is called one oscillation.
- The time taken for one oscillation is called the time period.
- The time period can be calculated by dividing the total measured time by the number of oscillations.
- Measuring several oscillations improves the reliability of pendulum timing.
- An object is in motion when its position changes with time relative to a reference point.
- Linear motion occurs along a straight path.
- Speed is the distance travelled per unit time.
- The SI unit of speed is metre per second.
- Distance can be calculated using speed multiplied by time.
- Time can be calculated using distance divided by speed.
- A speedometer measures speed, while an odometer records distance travelled.
- Uniform linear motion covers equal distances in equal intervals of time.
- Non-uniform linear motion covers unequal distances in equal intervals of time.
- Average speed is found by dividing total distance by total time.
- Tables and graphs can help us identify patterns of motion.
- Numerical answers involving physical quantities should always include appropriate units.