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Question
A vehicle moves along a straight line and covers a distance of 2 km. In the first 500 m, it moves with a speed of 10 m/s and in the next 500 m, it moves with a speed of 5 m/s. With what speed should it move the remaining distance so that the journey is complete in 200 s? What is the average speed of the vehicle for the entire journey?
🔗 Concepts: 8.3.1 Speed–Distance–Time | 8.3 Speed
Vehicle: 2 km in segments — find speed for third segment and average speed.
![Question 11 - A vehicle moves al - Measurement of Time an - [Teachoo] - Questions at the end of the chapter](https://cdn.teachoo.com/test/a699b893-c39d-4bc3-9010-0917574d5bfc/image-a-2-km-road-in-three-segments-500-m-at-10-m-s-500-m-at-5-m-s-1000-m-at-unknown-v-stopwatch-showing-200-s-total.png)
Show Answer
Speed of last segment = 20 m/s — average speed = 10 m/s
Explanation
📋 Given
- Segment 1: distance = 500 m, speed = 10 m/s
- Segment 2: distance = 500 m, speed = 5 m/s
- Segment 3: distance = 1000 m, speed = v (unknown)
- Total distance = 2000 m (= 2 km)
- Total time = 200 s
🔄 Unit Conversion
- No conversion needed — all distances in m, speeds in m/s.
📐 Formulas Used
Time = Distance ÷ Speed
Average Speed = Total Distance ÷ Total Time
Step 1 — Time for Segment 1
$$t_1 = \frac{500 \text{ m}}{10 \text{ m/s}} = 50 \text{ s}$$
Step 2 — Time for Segment 2
$$t_2 = \frac{500 \text{ m}}{5 \text{ m/s}} = 100 \text{ s}$$
Step 3 — Find time for Segment 3
Total time = 200 s. Time used = 50 + 100 = 150 s.
$$t_3 = 200 - 150 = 50 \text{ s}$$
Step 4 — Speed for last 1000 m
$$v = \frac{1000 \text{ m}}{50 \text{ s}} = \boxed{20 \text{ m/s}}$$
Step 5 — Average speed for whole journey
$$\text{Average speed} = \frac{2000 \text{ m}}{200 \text{ s}} = \boxed{10 \text{ m/s}}$$
Last segment v = 20 m/s — whole journey average speed = 10 m/s.
