Measurement of Time and MotionClass 7 Science NCERT Solutions

Given: Distance $= 150 \text{ m}$ Time $= 10 \text{ s}$

To Find: Speed in $\text{km/h}$

Formula: $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$

Calculation: $\text{Speed} = \frac{150 \text{ m}}{10 \text{ s}} = 15 \text{ m/s}$ To convert $\text{m/s}$ to $\text{km/h}$, we multiply by $\frac{3600}{1000} = \frac{18}{5}$ $\text{Speed} = 15 \times \frac{18}{5} \text{ km/h} = 54 \text{ km/h}$

Final Answer: The speed of the car is $54 \text{ km/h}$.

Given: Runner 1: Distance $= 400 \text{ m}$ Time $= 50 \text{ s}$ Runner 2: Distance $= 400 \text{ m}$ Time $= 45 \text{ s}$

To Find: Who has greater speed and by how much

Formula: $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$

Calculation: Speed of Runner 1: $S_1 = \frac{400 \text{ m}}{50 \text{ s}} = 8 \text{ m/s}$ Speed of Runner 2: $S_2 = \frac{400 \text{ m}}{45 \text{ s}} = 8.89 \text{ m/s}$ Difference in speed: $S_2 - S_1 = 8.89 - 8 = 0.89 \text{ m/s}$

Final Answer: Runner 2 has a greater speed by $0.89 \text{ m/s}$

Given: Speed $= 25 \text{ m/s}$ Distance $= 360 \text{ km} = 360000 \text{ m}$

To Find: Time taken

Formula: $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$

Calculation: $\text{Time} = \frac{360000 \text{ m}}{25 \text{ m/s}} = 14400 \text{ s}$ Converting seconds to hours: $\text{Time} = \frac{14400}{3600} \text{ h} = 4 \text{ h}$

Final Answer: The time taken is $4 \text{ h}$.

Given: Distance $= 180 \text{ km}$ Time $= 3 \text{ h}$

(i) To Find: Speed in $\text{km/h}$

Formula: $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$

Calculation: $\text{Speed} = \frac{180 \text{ km}}{3 \text{ h}} = 60 \text{ km/h}$

Final Answer: The speed of the train is $60 \text{ km/h}$.

(ii) To Find: Speed in $\text{m/s}$

Calculation: To convert $\text{km/h}$ to $\text{m/s}$, we multiply by $\frac{1000}{3600} = \frac{5}{18}$ $\text{Speed} = 60 \times \frac{5}{18} \text{ m/s} = \frac{300}{18} \text{ m/s} = 16.67 \text{ m/s}$

Final Answer: The speed of the train is $16.67 \text{ m/s}$.

(iii) To Find: Distance travelled in $4 \text{ h}$

Formula: $\text{Distance} = \text{Speed} \times \text{Time}$

Calculation: $\text{Distance} = 60 \text{ km/h} \times 4 \text{ h} = 240 \text{ km}$

Final Answer: The distance travelled in $4 \text{ h}$ is $240 \text{ km}$.

Given: Speed of horse $= 18 \text{ m/s}$ Speed of train $= 72 \text{ km/h}$

To Find: Comparison of speeds

Calculation: Convert the speed of the train to $\text{m/s}$: $\text{Speed of train} = 72 \times \frac{5}{18} \text{ m/s} = 20 \text{ m/s}$

Final Answer: The train is faster than the horse. The train's speed is $20 \text{ m/s}$, while the horse's speed is $18 \text{ m/s}$. The train is faster by $2 \text{ m/s}$.

Uniform Motion: Uniform motion is when an object moves along a straight line with a constant speed. This means the object covers equal distances in equal intervals of time. A car moving on a straight highway with no traffic can be an example of uniform motion if the driver maintains a constant speed.

Non-Uniform Motion: Non-uniform motion is when the speed of an object moving along a straight line keeps changing. This means the object covers unequal distances in equal intervals of time. A car moving in city traffic is an example of non-uniform motion because the driver constantly changes speed due to traffic conditions, signals, and other obstacles.

In uniform motion, the object covers equal distances in equal intervals of time. Here, in every 10 seconds, the object is covering a distance of 8 metres.

\begin{tabular}{|l|c|c|c|c|c|c|c|c|} \hline Time (s) & 0 & 10 & 20 & 30 & 40 & 50 & 60 & 70
\hline Distance (m) & 0 & 8 & 16 & 24 & 32 & 40 & 48 & 56
\hline \end{tabular}

The motion is not uniform because the car covers unequal distances in equal intervals of time (each hour).

Given: Distance in first hour $= 60 \text{ km}$ Distance in second hour $= 70 \text{ km}$ Distance in third hour $= 50 \text{ km}$ Total time $= 3 \text{ hours}$

To Find: Average speed

Formula: $\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}$

Calculation: $\text{Total Distance} = 60 + 70 + 50 = 180 \text{ km}$ $\text{Average Speed} = \frac{180 \text{ km}}{3 \text{ h}} = 60 \text{ km/h}$

Final Answer: The motion is non-uniform. The average speed of the car is $60 \text{ km/h}$.

Non-uniform motion is more common in daily life. This is because it is rare for objects to maintain a constant speed over long periods. Here are three examples:

The speed is non-uniform because the object covers unequal distances in equal intervals of time (10 seconds).

Given: Total distance $= 60 \text{ m}$ Total time $= 100 \text{ s}$

To Find: Average speed

Formula: $\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}$

Calculation: $\text{Average Speed} = \frac{60 \text{ m}}{100 \text{ s}} = 0.6 \text{ m/s}$

Final Answer: The speed is non-uniform. The average speed is $0.6 \text{ m/s}$.

Given: Total distance $= 2 \text{ km} = 2000 \text{ m}$ Total time $= 200 \text{ s}$ Distance 1 $= 500 \text{ m}$ Speed 1 $= 10 \text{ m/s}$ Distance 2 $= 500 \text{ m}$ Speed 2 $= 5 \text{ m/s}$ Distance 3 $= 2000 - 500 - 500 = 1000 \text{ m}$

To Find: Speed 3 and Average Speed

Calculations: Time 1 $= \frac{\text{Distance 1}}{\text{Speed 1}} = \frac{500 \text{ m}}{10 \text{ m/s}} = 50 \text{ s}$ Time 2 $= \frac{\text{Distance 2}}{\text{Speed 2}} = \frac{500 \text{ m}}{5 \text{ m/s}} = 100 \text{ s}$ Time 3 $= \text{Total time} - \text{Time 1} - \text{Time 2} = 200 - 50 - 100 = 50 \text{ s}$ Speed 3 $= \frac{\text{Distance 3}}{\text{Time 3}} = \frac{1000 \text{ m}}{50 \text{ s}} = 20 \text{ m/s}$ Average Speed $= \frac{\text{Total Distance}}{\text{Total Time}} = \frac{2000 \text{ m}}{200 \text{ s}} = 10 \text{ m/s}$

Final Answer: The required speed for the remaining distance is $20 \text{ m/s}$. The average speed for the entire journey is $10 \text{ m/s}$.