Measurement of Time and Motion — NCERT Solutions

Given: The object is in uniform motion, so it covers equal distances in equal time intervals.

Step 1: Find the speed (rate of distance covered)
From the table: In 10 s, distance covered = 8 m
$$\text{Speed} = \frac{8 \text{ m}}{10 \text{ s}} = 0.8 \text{ m/s}$$

Step 2: Verify with known values

• At t = 30 s: Distance = $0.8 \times 30 = 24$ m ✓
• At t = 50 s: Distance = $0.8 \times 50 = 40$ m ✓
• At t = 70 s: Distance = $0.8 \times 70 = 56$ m ✓

Step 3: Fill in the gaps

• At t = 20 s: Distance = $0.8 \times 20 = \mathbf{16 \text{ m}}$
• Missing time when Distance = 32 m: $t = \frac{32}{0.8} = \mathbf{40 \text{ s}}$
• At t = 60 s: Distance = $0.8 \times 60 = \mathbf{48 \text{ m}}$

Completed Table:

Given:

• Distance in 1st hour = 60 km
• Distance in 2nd hour = 70 km
• Distance in 3rd hour = 50 km

Is the motion uniform?
In uniform motion, equal distances must be covered in equal time intervals. Here, the distances covered in each hour are different (60 km, 70 km, 50 km). Since the distances are unequal in equal time intervals (1 hour each), the motion is non-uniform.

Average Speed:
$$\text{Total distance} = 60 + 70 + 50 = 180 \text{ km}$$
$$\text{Total time} = 1 + 1 + 1 = 3 \text{ h}$$
$$\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{180 \text{ km}}{3 \text{ h}} = 60 \text{ km/h}$$

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

Answer: Non-uniform motion is more common in daily life.

In most real-life situations, objects change their speed due to traffic, obstacles, turns, or varying forces. Perfectly constant speed over a long duration is rare.

Three examples of non-uniform motion from daily life:

1. A bus on a city road: A bus speeds up after a bus stop, slows down at traffic signals, and stops at the next bus stop. It covers unequal distances in equal time intervals.

2. A ball rolling on the ground: When a ball is rolled on the ground, it gradually slows down due to friction and eventually stops. Its speed keeps decreasing, so it covers unequal distances in equal time intervals.

3. A person walking: When a person walks, they may walk faster on an open path and slower in a crowded area or while climbing stairs. Their speed keeps changing, making the motion non-uniform.

Conclusion: Non-uniform motion is far more common in daily life because most moving objects experience changing forces (friction, air resistance, traffic, etc.) that cause their speed to vary.

Step 1: Check distances covered in each 10-second interval

The distances covered in equal time intervals (10 s each) are not equal. Therefore, the motion is non-uniform.

Step 2: Find average speed
$$\text{Total distance} = 60 \text{ m}$$
$$\text{Total time} = 100 \text{ s}$$
$$\text{Average speed} = \frac{60 \text{ m}}{100 \text{ s}} = 0.6 \text{ m/s}$$

Answer: The speed of the object is non-uniform. The average speed is $\mathbf{0.6 \text{ m/s}}$.

Given:

• Total distance = 2 km = 2000 m
• First 500 m at speed = 10 m/s
• Next 500 m at speed = 5 m/s
• Total time for journey = 200 s

Step 1: Find time taken for first 500 m
$$t_1 = \frac{500}{10} = 50 \text{ s}$$

Step 2: Find time taken for next 500 m
$$t_2 = \frac{500}{5} = 100 \text{ s}$$

Step 3: Find remaining time for the rest of the journey
$$t_3 = 200 - t_1 - t_2 = 200 - 50 - 100 = 50 \text{ s}$$

Step 4: Find remaining distance
$$\text{Remaining distance} = 2000 - 500 - 500 = 1000 \text{ m}$$

Step 5: Find required speed for remaining distance
$$v_3 = \frac{1000 \text{ m}}{50 \text{ s}} = 20 \text{ m/s}$$

Step 6: Find average speed for entire journey
$$\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{2000 \text{ m}}{200 \text{ s}} = 10 \text{ m/s}$$

Answers:

• The vehicle must cover the remaining 1000 m at a speed of $\mathbf{20 \text{ m/s}}$.
• The average speed for the entire journey is $\mathbf{10 \text{ m/s}}$.