Solutions-NCERT-Class-7-Science-Curiosity-Chapter-8-Measurement of Time and Motion-CBSE

Long ago, people measured time by observing natural events. They noticed events that happened again and again after fixed intervals.

Examples include:

• Rising and setting of the Sun
• Phases of the Moon
• Changing seasons

Measurement of a Day :

• People defined a day by the cycle of sunrise and sunset. The time between one sunrise and the next was considered one day.
• Sundials : To measure smaller parts of the day, people invented sundials. Sundials used the shadow formed by sunlight. The changing position of the shadow showed the time.
• Water Clocks : Water clocks measured time by the flow of water. Water slowly flowed into or out of a vessel. The movement of water helped people know the passing of time.
• Hourglasses : Hourglasses used sand to measure time. Sand flowed from one glass bulb to another through a narrow opening. The amount of sand that moved showed the time passed.
• Candle Clocks : Candle clocks used burning candles to measure time. Markings were made on the candle. As the candle burned down, the markings showed the passage of time.

Time Measuring in Ancient India :

• In ancient India, special devices were also used to measure time.
• One such device was the Ghatika−yantra.
• It was a water clock with a sinking bowl.
• Drums or gongs were used to announce standard units of time.

• To determine who is faster when distances are different, we calculate and compare the speed of each participant.
• Speed is calculated by taking the total distance covered and dividing it by the total time taken to cover that distance.

Formula : Speed = \(\frac{\text{Distance travelled }}{\text{Time taken}}\)

• Speed helps us know how much distance an object covers in a unit of time. The unit of time can be: one second, one minute, or one hour.
• The runner who covers the maximum distance in that specific unit of time is the one with the highest speed and is considered the fastest.

• The difference in their motion depends on whether their speed remained constant or changed as they moved along the straight path.
• Runners who maintained a constant, unchanging speed were in uniform linear motion, meaning they covered equal distances in equal intervals of time.
• On the other hand, runners who sped up or slowed down were in non−uniform linear motion.
• In non−uniform motion, the speed of the object keeps changing, resulting in unequal distances being covered over equal time intervals.
• Uniform linear motion is mostly an ideal situation. Most motions in daily life are non−uniform.
• Since speed often changes during motion, we usually calculate average speed to describe a journey.

Average Speed = \(\frac{\text{Total distance travelled }}{\text{Total time taken}}\)

Given Values :

• Distance = 150 metres
• Time = 10 seconds

Formula : Speed = \(\frac{\text{Distance travelled }}{\text{Time taken}}\)

∴ Speed of car = \(\frac{150\,m}{10\,s}\) = 15 m/s

Conversion Factor: To convert m/s to km/h, multiply by 18/5.

∴ 15 m/s × \(\frac{18}{5}\) = 54 km/h

Let’s calculate the speed of both runners and then compare them.

Formula : Speed = \(\frac{\text{Distance travelled }}{\text{Time taken}}\)

Calculation for the First Runner :

• Distance = 400 metres
• Time = 50 seconds

∴ Speed = \(\frac{400\,m}{50\,s}\) = 8 m/s

Calculation for the Second Runner :

• Distance = 400 metres
• Time = 45 seconds

∴ Speed = \(\frac{400\,m}{45\,s}\)  ≈ 8.89 m/s

The second runner is faster because they have a higher speed (8.89 m/s compared to 8 m/s).

Difference in speed: 8.89 m/s − 8 m/s = 0.89 m/s.

Final Answer: The second runner is faster by 0.89 m/s.

We need to calculate the time taken by a train using its speed and the distance covered.

Given Values :

• Speed = 25 m/s
• Distance = 360 km

Formula : Time = \(\frac{Distance Travelled}{Speed}\)

Converting Speed to km/h:

To convert m/s to km/h, we multiply by 18/5

Speed in km/h = 25 m/s × \(\frac{18}{5}\) = 90 km/h

Calculating Time take :

∴ Time = \(\frac{360\,km}{90\,km/h}\) = 4 hours

Final Answer: The train takes 4 hours to cover the distance.

Using the relationships between speed, distance, and time.

(i) Find Speed in km/h :

Given:

• Total distance covered = 180 km
• Total time taken = 3 h

Speed = \(\frac{\text{Distance travelled }}{\text{Time taken}}\) = \(\frac{180\,km}{3\,h}\) = 60 km/h

(ii) Find Speed in m/s :

To convert the speed km/h to metres per second (m/s), we use the following standard conversions:

• 1 km = 1,000 meters
• 1 hour = 3,600 seconds (60 min × 60 s)

Calculation:

• 60 km/h = \(\frac{60×1000\,m}{3600\,s}\)  = 16.67 m/s

(iii) Find distance travelled in 4 hours :

• Train speed : 60 km/h
• Time : 4 hours

Total Distance travelled = Speed × Time = 60 km/h × 4 h = 240 km

Final Answers:

• (i) Speed in km/h = 60 km/h
• (ii) Speed in m/s ≈ 16.67 m/s
• (iii) Distance travelled in 4 h = 240 km

We must compare the speeds of a galloping horse and a train. To do this accurately, we need to convert them into the same units.

Given Values :

• Speed of the horse = 18 m/s
• Speed of the train = 72 km/h

Unit Conversion :

To compare these two, we can convert the train's speed from kilometres per hour (km/h) to metres per second (m/s) using the standard conversion method:

• 1 km = 1,000 meters
• 1 hour = 3,600 seconds (60 min × 60 s)

Calculation for Train Speed in m/s:

Speed of train = \(\frac{72×1000\,m}{3600\,s}\)  = 20 m/s

Now that both speeds are in the same units, we can compare them directly:

• Horse: 18 m/s
• Train: 20 m/s

The train is faster than the horse because its speed (20 m/s) is higher than the horse's speed (18 m/s).

Difference in speed = 20 – 18 = 2 m/s

Final Answer: The train is faster than the galloping horse by 2 m/s

Determine the Constant Speed :

To fill the gaps, we first need to find the speed of the object using a complete pair of time and distance from the table.

We use the formula:  Speed =

Using the first non−zero data point:

• Distance = 8 metres
• Time = 10 seconds

∴ Speed = \(\frac{\text{Distance travelled }}{\text{Time taken}}\) = \(\frac{8\,m}{10\,s}\) = 0.8 m/s

Since the motion is uniform, this speed of 0.8 m/s remains constant throughout the journey.

Finding the missing values :

Using the constant speed (0.8 m/s), we can calculate the missing values.

Missing value 1 (Find distance for Time = 20 s):

Distance = Speed × Time = 0.8 m/s × 20 s = 16 m

Missing value 2 (Find time for Distance = 32 m):

Time = \(\frac{Distance Travelled}{Speed}\) = \(\frac{32\,m}{0.8\,m/s}\) = 40 s

Completed Table :

Final Answer: The missing values are 16 m (at 20 seconds) and 40 s (for 32 metres).

(i) No, the motion is non−uniform.

Justification :

An object is in uniform linear motion only if it covers equal distances in equal intervals of time. In this case:

• In the first hour, the car covers 60 km.
• In the second hour, the car covers 70 km.
• In the third hour, the car covers 50 km.

Since the distances covered in each equal one−hour interval are different (60 km ≠ 70 km ≠ 50 km), the speed is changing, and the motion is non−uniform.

(ii) Calculation of Average Speed :

Given :

• Total distance = 60 km + 70 km + 50 km = 180 km
• Total time = 1 h + 1 h + 1 h = 3 h

Formula : Average Speed = \(\frac{\text{Total distance travelled }}{\text{Total time taken}}\)

∴ Average Speed = \(\frac{180\,km}{3\,h}\) = 60 km/h

Final Answer: The motion is non−uniform because the car covers unequal distances in equal intervals of time. The average speed of the car is 60 km/h.

In daily life, non−uniform linear motion is much more common than uniform motion.

Justification :

• In daily life, non−uniform linear motion is more common than uniform motion.
• Uniform motion means moving with a constant speed.
• It is mostly an ideal situation and is rarely seen for long periods.
• In real life, the speed of moving objects usually changes.
• Therefore, we often use average speed to describe motion.

Examples of Non−Uniform Motion :

(i) Train Journey :

• A train starts slowly from a station. It then speeds up while moving.
• Before reaching the next station, it slows down again.
• Since the speed keeps changing, the motion is non−uniform.

(ii) Running a Marathon :

• Marathon runners do not run at the same speed all the time.
• They may run faster when energetic and slower when tired.
• Because their speed changes, the motion is non−uniform.

(iii) Cycling in a Neighborhood :

• A cyclist changes speed while taking turns or avoiding obstacles.
• Speed also changes on uphill and downhill roads.
• Therefore, cycling is an example of non−uniform motion.

The motion of the object is non−uniform.

Justification :

An object is in uniform linear motion only if it covers equal distances in equal intervals of time. In the provided table, the time intervals are equal (every 10 seconds), but the distances covered in those intervals vary:

• 0 to 10 s: covers  6 − 0 = 6 m
• 10 to 20 s: covers 10 – 6 = 4 m
• 20 to 30 s: covers 16 – 10 = 6 m
• 30 to 40 s: covers 21 – 16 = 5 m
• ...and so on.

Because the object covers unequal distances in equal intervals of time, its speed is changing, making it non−uniform linear motion.

Calculation of Average Speed :

Using the final values from the table:

• Total distance covered = 60 metres
• Total time taken = 100 seconds

Average Speed = \(\frac{\text{Total distance travelled }}{\text{Total time taken}}\) = \(\frac{60\,m}{100\,s}\) = 0.6 m/s

Final Answer: The motion is non−uniform because the distances covered in each 10−second interval are not equal. The average speed of the object is 0.6 m/s.

Given :

• Total Distance: 2 km = 2000 m
• Target Total Time: 200 seconds
• Speed for first 500 m: 10 m/s
• Speed for next 500 m: 5 m/s

(i) Calculate Time for the First Two Segments :

Formula : Time = \(\frac{Distance Travelled}{Speed}\)

• First 500 m:

Time 1 = \(\frac{500}{10}\) = 50 s

• Next 500 m:

Time 2 = \(\frac{500}{5}\) = 100 s

Total time used so far: 50 s + 100 s = 150 s

(ii) Determine the Required Speed for the Remaining Distance :

First, we find the remaining distance and the time left to reach the 200−second goal.

• Remaining Distance: 2,000 m – (500 m + 500 m) = 1,000 metres
• Remaining Time: 200 s − 150 s = 50 seconds

Now, we use the speed formula: Speed = \(\frac{\text{Distance travelled }}{\text{Time taken}}\)

Required Speed for last 1000 m = \(\frac{1000\,m}{50\,s}\) = 20 m/s

(iii) Calculate the Average Speed for the Entire Journey :

Average Speed = \(\frac{\text{Total distance travelled }}{\text{Total time taken}}\) = \(\frac{2000\,m}{200\,s}\) = 10 m/s

Final Answer:

• The vehicle should move the remaining distance at a speed of 20 m/s.
• The average speed for the entire journey is 10 m/s.