GSEB Class 7 Science Solutions Chapter 13 ગતિ અને સમય

Textbook Exercise Questions and Answers

 

Question 1. Classify the following motions as linear motion, circular motion, or oscillatory motion:
(i) The motion of your hands while running.
(ii) The motion of a bullock pulling a cart on a straight road.
(iii) The motion of a child.
(iv) The motion of the hammer of an electric bell.
(v) The motion of a train passing over a straight bridge.
Answer:
(i) The motion of hands while running is oscillatory motion.
(ii) The motion of a bullock pulling a cart on a straight road is linear motion.
(iii) The motion of a child is oscillatory motion.
(iv) The motion of the hammer of an electric bell is oscillatory motion.
(v) The motion of a train passing over a straight bridge is linear motion.
In simple words: Look at how things move. If it goes back and forth like a swing, it's oscillatory. If it goes in a straight line, it's linear. If it goes in a circle, it's circular.

Exam Tip: Remember to clearly distinguish between repetitive back-and-forth motion (oscillatory) and motion along a straight path (linear).

 

Question 2. Which of the following statements are not true?
(1) The basic unit of time is the second.
(2) Every object moves with a constant speed.
(3) The distance between two cities is measured in kilometers.
(4) The time period of a given pendulum is not constant.
(5) The speed of a train is measured in m/h.
Answer: The statements that are not true are: (2), (4), (5).
In simple words: Only statements (2), (4), and (5) are incorrect from the list. The other statements are correct.

Exam Tip: Carefully read each statement and consider common misconceptions about motion and units. For instance, speed is often variable, and the time period of a simple pendulum is generally constant for small oscillations.

 

Question 3. A simple pendulum takes 32 seconds to complete 20 oscillations. What is the time period of the pendulum?
Answer:
Time taken to complete 20 oscillations \( = 32 \) seconds.
Therefore, time taken to complete 1 oscillation \( = \frac{32}{20} \) seconds
\( = \frac{16}{10} = 1.6 \) seconds
The time taken to complete 1 oscillation is the time period.
So, the time period \( = 1.6 \) seconds.
In simple words: To find out how long one swing takes, divide the total time by the number of swings. This gives you the time period for each swing.

Exam Tip: The time period of a simple pendulum is calculated by dividing the total time for a number of oscillations by the count of those oscillations. Ensure your units are consistent.

 

Question 4. The distance between two stations is 240 km. A train takes 4 hours to cover this distance. Find the speed of this train.
Answer:
Distance covered \( = 240 \) km
Time taken \( = 4 \) hours
Now, the speed of the train \( = \frac{\text{Total distance covered}}{\text{Time taken}} \)
\( = \frac{240 \text{ km}}{4 \text{ hours}} \)
\( = 60 \text{ km/hour} \)
In simple words: To calculate how fast the train is moving, divide the total distance it travels by the total time it takes to cover that distance.

Exam Tip: Always remember the basic formula for speed: Speed = Distance/Time. Make sure to use consistent units for distance and time.

 

Question 5. When the clock shows 8:30 am, the odometer reading of a car is 37321.0 km. When the clock shows 8:50 am, the odometer reading of the car is 57336.0 km. Find the speed of the car in km/min and km/h during this period.
Answer:
Distance covered by the car \( = \) Final reading \( - \) Initial reading
\( = 57336.0 \text{ km} - 57321.0 \text{ km} \)
\( = 15 \text{ km} \)
Time taken by the car \( = \) Time from 8:30 am to 8:50 am
\( = 20 \) minutes (min).
Speed of the car \( = \frac{\text{Distance covered}}{\text{Time taken}} \)
\( = \frac{15 \text{ km}}{20 \text{ min}} \)
\( = \frac{5 \times 3}{5 \times 4} \text{ km/min} \)
\( = 0.75 \text{ km/min} \) (1)
To convert to km/h, multiply the minutes by \( \frac{1}{60} \) or multiply the km/min by 60.
Speed \( (\text{km/h}) = \frac{15 \text{ km}}{(20/60) \text{ h}} \)
\( = \frac{15 \times 60}{20} \text{ km/h} \)
\( = 45 \text{ km/h} \) (2)
In simple words: First, find the distance traveled by subtracting the start odometer reading from the end reading. Then, find the time taken. Divide the distance by time to get speed in km/min, and convert that to km/h by multiplying by 60.

Exam Tip: Pay close attention to unit conversions, especially when moving between minutes and hours. Always ensure the time difference is correctly calculated.

 

Question 6. Salma reaches her school from home in 15 minutes by bicycle. If the speed of the bicycle is 2 m/s, find the distance between her home and school.
Answer:
Time taken \( = 15 \) minutes \( = (15 \times 60) \) seconds \( = 900 \) s
Speed of the bicycle \( = 2 \) m/s
Therefore, the distance covered by Salma \( = \) Speed \( \times \) Time
\( = (2 \text{ m/s} \times 900 \text{ s}) \)
\( = 1800 \text{ m} \)
\( = \frac{1800}{1000} \text{ km} = 1.800 \text{ km} \)
So, the distance between home and school \( = 1.8 \) kilometers.
In simple words: To find how far Salma traveled, multiply her speed by the time she took. Remember to change minutes into seconds first, then convert meters to kilometers.

Exam Tip: Before calculations, always convert all quantities to consistent units (e.g., meters and seconds, or kilometers and hours) to avoid errors.

 

Question 7. In the following cases, show the shape of the distance-time graph:
(1) A car moving at constant speed.
(2) A car standing on the side of the road.
Answer:
(1) A car moving at constant speed:

(2) A car standing on the side of the road:

In simple words: For constant speed, the graph shows a straight line sloping up. For an object standing still, the graph is a flat, horizontal line, because the distance from the start point does not change over time.

Exam Tip: A distance-time graph with a straight line shows constant speed. A horizontal line means the object is at rest. A curved line indicates changing speed (acceleration or deceleration).

 

Question 8. Which of the following relationships is correct?
(a) Speed = Distance X Time
(b) Speed = Distance / Time
(c) Speed = Time / Distance
(d) Speed = 1 / (Distance X Time)
Answer: (b) Speed = Distance / Time
In simple words: Speed tells us how quickly something moves. We calculate it by dividing the total distance traveled by the time it took to travel that distance.

Exam Tip: Always remember the fundamental formula for speed. It's a key concept in physics and is used frequently in calculations.

 

Question 9. The basic unit of speed is __________ .
(a) km/min
(b) m/min
(c) km/h
(d) m/s
Answer: (d) m/s
In simple words: The standard unit for measuring speed in science is meters per second, known as m/s.

Exam Tip: The SI unit (International System of Units) for speed is meters per second (m/s). While other units like km/h are common, m/s is the fundamental unit.

 

Question 10. A car travels at a speed of 40 km/h for 15 minutes and then at a speed of 60 km/h for another 15 minutes. Find the total distance covered by the car.
Answer:
Calculation:
Distance covered by the car in the first 15 minutes \( = \) Speed \( \times \) Time
\( = (40 \text{ km/h} \times \frac{15}{60} \text{ h}) \)
\( = 10 \text{ km} \)
Distance covered by the car in the next 15 minutes \( = \) Speed \( \times \) Time
\( = (60 \text{ km/h} \times \frac{15}{60} \text{ h}) \)
\( = 15 \text{ km} \)
Therefore, the total distance covered by the car \( = 10 \text{ km} + 15 \text{ km} = 25 \text{ km} \).
In simple words: First, calculate the distance for each part of the journey using speed and time. Make sure to convert minutes to hours. Then, simply add those distances together to get the total distance traveled.

Exam Tip: When dealing with multiple segments of a journey, calculate the distance for each segment separately before adding them up. Always convert time units to match the speed units.

 

Question 11. Two photographs shown in Figure 13.2 are taken at an interval of 10 s. If a distance of 100 m is represented by 1 cm in these photographs, calculate the speed of the fastest car.
Answer:
Looking at Figures 13.1 and 13.2 from the textbook, the distance measured for the blue car in two photographs is 1 cm.
Also, 1 cm \( = 100 \) meters on the scale.
Therefore, the distance covered by the blue car \( = 100 \) meters.
Now, the two photographs are taken at an interval of 10 seconds.
So, the distance covered by the blue car in 10 seconds \( = 100 \) meters.
Therefore, the distance covered by the blue car in 1 second \( = \frac{100 \text{ meters}}{10 \text{ seconds}} \)
\( = 10 \text{ m/s} \)
So, the speed of the blue car \( = 10 \) m/s.
(Note: In Figure 13.1, the blue car is near the white line on the left side of the road.)
In simple words: We know the scale of the photo. We measure how far the car moved in the photo and use the scale to find the real distance. Then, divide that real distance by the time between photos to get the car's speed.

Exam Tip: When using scale drawings or photographs, always convert measured distances to real-world distances using the given scale factor before performing any calculations.

 

Question 12. The following figure shows the distance-time graph for two vehicles A and B. Which of these vehicles is moving faster?

Answer: Vehicle A moves faster.
Reason: To find the distance covered by vehicle B and vehicle A at a specific time, draw a line parallel to the Y-axis from time 't' on the X-axis. The vehicle with the greater height (steeper slope) on the graph is moving faster.
In simple words: On a distance-time graph, the line that goes up more steeply shows an object moving faster. Since line A is steeper than line B, vehicle A is moving more quickly.

Exam Tip: In a distance-time graph, the slope of the line represents speed. A steeper slope indicates higher speed, while a less steep slope indicates lower speed. A horizontal line means the object is at rest.

 

Question 13. Which of the given distance-time graphs for a truck's motion shows that the truck's speed is not constant?

Answer: Graph (iii) is a curved line.
Graph (iii) shows that the speed is not constant.
In simple words: If a graph of distance versus time is a curved line, it means the speed is always changing, not staying the same.

Exam Tip: A curved line on a distance-time graph indicates that the object's speed is changing (it is accelerating or decelerating). A straight, sloped line shows constant speed, and a horizontal line shows the object is at rest.

Understanding Textbook Activities

 

Activity 1: To be done independently.
Answer: This activity involves practical work and observation that students should perform on their own. It might require setting up an experiment or making direct observations in a real-world setting. Students will gain practical understanding by doing it themselves.
In simple words: This task is for you to do on your own. It's a hands-on activity to learn by doing.

Exam Tip: For practical activities, focus on understanding the core concept and the procedure, even if you don't perform the exact experiment. Think about what you would observe and conclude.

 

Activity 2: To determine the time period of a simple pendulum.
Materials: A string approximately 1 meter long, a pendulum bob (with a hook), a stopwatch.

Procedure:
1. Construct a pendulum as shown in the figure, using a string about 1 meter long.
2. Allow the pendulum bob to come to rest at its mean position O. Mark this basic position on the ground below it.
3. To set the pendulum in motion, gently hold the pendulum bob and pull it slightly to one side, say to position A.
4. Now, release the bob from its displaced position. Make sure not to push it.
5. Start the stopwatch to note the time when the bob reaches the extreme position A on one side.
6. Consider one oscillation complete when the pendulum returns to position A again.
7. In this way, when 20 oscillations are completed, stop the stopwatch immediately. Note the time taken for 20 oscillations from the stopwatch. Record your observations in Table 13.2. Divide your observed time by 20 to write the time period.
Answer:

Observation: When finding the time period of a pendulum using a string of a specific length, the time period comes out to be almost the same every time.
Conclusion: The time period of a pendulum of a specific length is fixed.
In simple words: This activity shows that if you use the same length of string for a pendulum, it will always take about the same amount of time to complete one swing. This time is called the time period.

Exam Tip: Understanding the setup and purpose of a simple pendulum experiment is crucial. The key takeaway is that the time period depends on the length of the pendulum, not its mass or the amplitude of oscillation (for small angles).

 

Activity 3: To calculate the speed of a rolling ball.
Materials: Ball, stopwatch.