A bus is moving with a speed of `10 m s^(-1)` on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooteritst with what speed should the scooterist chase the bus?

Options

A. `40 m s^(-1)`
B. `25 m s^(-1)`
C. `10 m s^(-1)`
D. `20 m s^(-1)`

Explanation

To solve the problem, we need to find the speed at which the scooterist should travel to overtake the bus in a given time. Let's break down the solution step by step.

### Step-by-Step Solution:

1. **Identify Given Information:**
- Speed of the bus (VB) = 10 m/s
- Distance from the scooterist to the bus = 1 km = 1000 m
- Time to overtake (t) = 100 s

2. **Understanding the Problem:**
- The scooterist wants to cover the distance of 1000 m and also gain on the bus, which is moving at 10 m/s.
- The scooterist needs to travel faster than the bus to overtake it.

3. **Relative Speed Concept:**
- The relative speed of the scooterist with respect to the bus when both are moving in the same direction is given by:
\[ \text{Relative Speed} = V_s - V_b \]
where \( V_s \) is the speed of the scooterist.

4. **Using the Formula for Distance:**
- The distance covered by the scooterist to overtake the bus can be expressed using the formula:
\[ \text{Distance} = \text{Relative Speed} \times \text{Time} \]
- Substituting the known values:
\[ 1000 = (V_s - 10) \times 100 \]

5. **Rearranging the Equation:**
- Simplifying the equation:
\[ 1000 = 100V_s - 1000 \]
- Adding 1000 to both sides:
\[ 2000 = 100V_s \]

6. **Solving for Scooter Speed:**
- Dividing both sides by 100:
\[ V_s = \frac{2000}{100} = 20 \text{ m/s} \]

7. **Conclusion:**
- The speed at which the scooterist should chase the bus is **20 m/s**.

### Final Answer:
The scooterist should chase the bus at a speed of **20 m/s**.