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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, 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 for the entire journey?
Answer.
Step 1 - Time for first 500 m
Use the formula: Time = Distance ÷ Speed
$$\begin{aligned} t_1 &= \frac{\text{Distance}}{\text{Speed}} \\[8pt] &= \frac{500 \text{ m}}{10 \text{ m/s}} \\[8pt] &= 50 \text{ s} \end{aligned}$$
Step 2 - Time for next 500 m
$$\begin{aligned} t_2 &= \frac{\text{Distance}}{\text{Speed}} \\[8pt] &= \frac{500 \text{ m}}{5 \text{ m/s}} \\[8pt] &= 100 \text{ s} \end{aligned}$$
Step 3 - Time left for remaining distance
- Total journey time = 200 s
- Time used so far = 50 + 100 = 150 s
- Time left = 200 − 150 = 50 s
Step 4 - Remaining distance
- Total distance = 2 km = 2000 m
- Distance covered so far = 1000 m
- Distance left = 1000 m
Step 5 - Required speed for remaining distance
Use the formula: Speed = Distance ÷ Time
$$\begin{aligned} \text{Speed} &= \frac{\text{Distance}}{\text{Time}} \\[8pt] &= \frac{1000 \text{ m}}{50 \text{ s}} \\[8pt] &= 20 \text{ m/s} \end{aligned}$$
Step 6 - Average speed for entire journey
Use the formula: Average speed = Total distance ÷ Total time
$$\begin{aligned} \text{Average speed} &= \frac{\text{Total distance}}{\text{Total time}} \\[8pt] &= \frac{2000 \text{ m}}{200 \text{ s}} \\[8pt] &= 10 \text{ m/s} \end{aligned}$$
The vehicle must move at 20 m/s for the remaining distance. The average speed of the entire journey is 10 m/s .
