A scooterist sees a bus 1 km ahead of him moving with a velocity of `10 ms^(-1)` With what speed the scooterist should move so as to overtake the bus in 100 s?

Options

A. `10 ms ^(-1)`
B. `20 ms ^(-1)`
C. `50 ms ^(-1)`
D. `30 ms ^(-1)`

Explanation

To solve the problem, we need to determine the speed at which the scooterist must travel to overtake the bus in 100 seconds. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the scenario
- The bus is initially 1 km (1000 meters) ahead of the scooterist.
- The bus is moving with a velocity of 10 m/s.
- We need to find the speed of the scooterist (let's denote it as \( v_s \)) so that he overtakes the bus in 100 seconds.

### Step 2: Calculate the distance traveled by the bus in 100 seconds
- The distance traveled by the bus can be calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
- For the bus:
\[ \text{Distance}_{\text{bus}} = 10 \, \text{m/s} \times 100 \, \text{s} = 1000 \, \text{meters} \]

### Step 3: Determine the total distance the scooterist needs to cover
- Initially, the bus is 1000 meters ahead. In 100 seconds, the bus will travel another 1000 meters.
- Therefore, the total distance the scooterist needs to cover to overtake the bus is:
\[ \text{Total Distance} = 1000 \, \text{meters (initial distance)} + 1000 \, \text{meters (distance traveled by bus)} = 2000 \, \text{meters} \]

### Step 4: Calculate the speed required for the scooterist
- The speed of the scooterist can be calculated using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
- Plugging in the values:
\[ v_s = \frac{2000 \, \text{meters}}{100 \, \text{seconds}} = 20 \, \text{m/s} \]

### Conclusion
- The scooterist must travel at a speed of **20 m/s** to overtake the bus in 100 seconds.

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