A bus is moving with a speed of `10 ms^-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 scooterist with what speed should the scooterist chase the bus ?

Options

A. a. `10 m s^(-1)`
B. b. `20 m s^(-1)`
C. c. `50 m s^(-1)`
D. d. `30 m s^(-1)`

Answer

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

### Step 1: Understand the Given Information
- Speed of the bus (Vb) = 10 m/s
- Distance from the scooterist to the bus = 1 km = 1000 m
- Time to overtake the bus (t) = 100 s

### Step 2: Define the Speed of the Scooterist
Let the speed of the scooterist be Vs (in m/s).

### Step 3: Calculate the Relative Velocity
The relative velocity of the scooterist with respect to the bus is given by:
\[ V_{relative} = V_s - V_b \]
Substituting the value of Vb:
\[ V_{relative} = V_s - 10 \]

### Step 4: Use the Relative Motion Formula
The formula for relative motion is:
\[ V_{relative} = \frac{D_{relative}}{t} \]
Where:
- \( D_{relative} \) is the relative distance (1000 m)
- \( t \) is the time (100 s)

Substituting the values:
\[ V_{relative} = \frac{1000 \, \text{m}}{100 \, \text{s}} = 10 \, \text{m/s} \]

### Step 5: Set Up the Equation
Now we can set the equation for relative velocity:
\[ V_s - 10 = 10 \]

### Step 6: Solve for Vs
To find the speed of the scooterist (Vs):
\[ V_s = 10 + 10 \]
\[ V_s = 20 \, \text{m/s} \]

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

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