Questions: t0=0, u1=20 m / s, u2=10 m / s

Transcript text: $t_{0}=0$, $u_{1}=20 \mathrm{~m} / \mathrm{s}$, $u_{2}=10 \mathrm{~m} / \mathrm{s}$

Solution

Solution Steps

Step 1: Understanding the Problem

We have two vehicles moving in the same direction with initial velocities $ u_1 = 20 \, \text{m/s} $ and $ u_2 = 10 \, \text{m/s} $. The problem provides three possible initial distances between the vehicles: 1000 m, 6000 m, and 2000 m. We need to determine which of these distances is relevant based on the given information.

Step 2: Analyzing the Motion

Since both vehicles are moving in the same direction, we can analyze their relative motion. The relative velocity of vehicle 1 with respect to vehicle 2 is:

\[ v_{\text{relative}} = u_1 - u_2 = 20 \, \text{m/s} - 10 \, \text{m/s} = 10 \, \text{m/s} \]

This means vehicle 1 is moving 10 m/s faster than vehicle 2.

Step 3: Determining the Relevant Distance

To determine the relevant initial distance, we need to consider the context or additional information that might be missing from the problem statement. However, since the problem does not provide further context, we can only state the relative velocity and the possible initial distances.

Final Answer

Since the problem does not provide enough context to determine which initial distance is correct, we can only list the possible initial distances:

1000 m
6000 m
2000 m

Without additional information, we cannot definitively choose one. However, if the problem intended to ask which distance would allow vehicle 1 to catch up to vehicle 2 in a specific time, more information would be needed.

Thus, the final answer is:

\[ \boxed{\text{Possible initial distances: 1000 m, 6000 m, 2000 m}} \]

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