A bus begins to move with an acceleration of ` 1 ms^(-1)` . A man who is `1 48m` behind the bus starts running at ` 10 ms^(-1)` to catch the bus, the man will be able to catch the bus after .

Options

A. ` 6 s`
B. ` 12 s`
C. ` 8 s`
D. ` 4 s`

Explanation

To solve the problem step by step, we will analyze the motion of both the bus and the man, and then find out when the man catches up to the bus.

### Step 1: Understand the motion of the bus
The bus starts from rest and accelerates at a rate of \(1 \, \text{m/s}^2\).
- Initial velocity of the bus, \(u_b = 0 \, \text{m/s}\)
- Acceleration of the bus, \(a_b = 1 \, \text{m/s}^2\)

### Step 2: Write the equation of motion for the bus
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