Measurement of Time and Motion

Given:
- Distance = 150 m
- Time = 10 s

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

Step 1: Find speed in m/s
$$\text{Speed} = \frac{150 \text{ m}}{10 \text{ s}} = 15 \text{ m/s}$$

Step 2: Convert m/s to km/h
$$1 \text{ m/s} = \frac{3600}{1000} \text{ km/h} = 3.6 \text{ km/h}$$
$$\text{Speed} = 15 \times 3.6 = 54 \text{ km/h}$$

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

Given:
- Runner 1: Distance = 400 m, Time = 50 s
- Runner 2: Distance = 400 m, Time = 45 s

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

Speed of Runner 1:
$$v_1 = \frac{400}{50} = 8 \text{ m/s}$$

Speed of Runner 2:
$$v_2 = \frac{400}{45} = \frac{80}{9} \approx 8.89 \text{ m/s}$$

Comparison:
Since $v_2 > v_1$, Runner 2 is faster.

Difference in speed:
$$v_2 - v_1 = \frac{80}{9} - 8 = \frac{80 - 72}{9} = \frac{8}{9} \approx 0.89 \text{ m/s}$$

Answer: Runner 2 has a greater speed. Runner 2 is faster than Runner 1 by approximately $\mathbf{\frac{8}{9} \approx 0.89 \text{ m/s}}$.

Given:
- Speed = 25 m/s
- Distance = 360 km

Step 1: Convert distance to metres
$$360 \text{ km} = 360 \times 1000 = 360000 \text{ m}$$

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

Step 2: Calculate time
$$\text{Time} = \frac{360000 \text{ m}}{25 \text{ m/s}} = 14400 \text{ s}$$

Step 3: Convert to hours
$$14400 \text{ s} = \frac{14400}{3600} \text{ h} = 4 \text{ h}$$

Answer: The train takes $\mathbf{14400 \text{ s}}$ (i.e., 4 hours) to cover 360 km.

Given:
- Distance = 180 km
- Time = 3 h

(i) Speed in km/h:
$$\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{180 \text{ km}}{3 \text{ h}} = 60 \text{ km/h}$$

(ii) Speed in m/s:
$$60 \text{ km/h} = \frac{60 \times 1000}{3600} \text{ m/s} = \frac{60000}{3600} = \frac{50}{3} \approx 16.67 \text{ m/s}$$

(iii) Distance in 4 h at the same speed:
$$\text{Distance} = \text{Speed} \times \text{Time} = 60 \text{ km/h} \times 4 \text{ h} = 240 \text{ km}$$

Answers:
- (i) Speed = $\mathbf{60 \text{ km/h}}$
- (ii) Speed = $\mathbf{\frac{50}{3} \approx 16.67 \text{ m/s}}$
- (iii) Distance in 4 h = $\mathbf{240 \text{ km}}$

Given:
- Speed of horse = 18 m/s
- Speed of train = 72 km/h

Step 1: Convert train speed to m/s
$$72 \text{ km/h} = \frac{72 \times 1000}{3600} \text{ m/s} = \frac{72000}{3600} = 20 \text{ m/s}$$

Step 2: Compare
- Speed of horse = 18 m/s
- Speed of train = 20 m/s

$$\text{Difference} = 20 - 18 = 2 \text{ m/s}$$

Answer: The train is faster than the fastest galloping horse. The train moves at 20 m/s while the horse moves at 18 m/s, so the train is faster by $\mathbf{2 \text{ m/s}}$.

Uniform Motion:
When an object covers equal distances in equal intervals of time, it is said to be in uniform motion.

*Example:* A car moving on a straight highway with no traffic maintains a constant speed (say 80 km/h). It covers equal distances in equal time intervals. This is uniform linear motion.

Non-Uniform Motion:
When an object covers unequal distances in equal intervals of time, it is said to be in non-uniform motion.

*Example:* A car moving in city traffic has to slow down at signals, speed up on clear stretches, and stop at crossings. It covers different distances in equal time intervals. This is non-uniform motion.

| Feature | Uniform Motion | Non-Uniform Motion |
|---|---|---|
| Speed | Constant | Keeps changing |
| Distance in equal time | Equal | Unequal |
| Example | Car on empty highway | Car in city traffic |