Starting from a stationary position , Rahul paddles his bicycle to attain a velocity of `6 m//s` in `30 s`. Then he applies brakes such that the velocity of bicycle comes down to `4m//s` in the next `5s` . Calculate the acceleration of the bicycle in both the cases.

Explanation

To solve the problem, we need to calculate the acceleration of the bicycle in two different cases: when Rahul accelerates to a velocity of 6 m/s and when he decelerates to a velocity of 4 m/s.

### Step-by-Step Solution:

**Case 1: Acceleration to 6 m/s**

1. **Identify initial and final velocities**:
- Initial velocity (u) = 0 m/s (starting from stationary)
- Final velocity (v) = 6 m/s

2. **Identify the time taken**:
- Time (t) = 30 s

3. **Use the formula for acceleration**:
\[ a = \frac{v - u}{t} \]
Substituting the values:
\[ a = \frac{6 \, \text{m/s} - 0 \, \text{m/s}}{30 \, \text{s}} = \frac{6}{30} = 0.2 \, \text{m/s}^2 \]

**Case 2: Deceleration to 4 m/s**

1. **Identify initial and final velocities**:
- Initial velocity (u) = 6 m/s (before applying brakes)
- Final velocity (v) = 4 m/s

2. **Identify the time taken**:
- Time (t) = 5 s

3. **Use the formula for acceleration**:
\[ a = \frac{v - u}{t} \]
Substituting the values:
\[ a = \frac{4 \, \text{m/s} - 6 \, \text{m/s}}{5 \, \text{s}} = \frac{-2}{5} = -0.4 \, \text{m/s}^2 \]

### Summary of Results:
- **Acceleration during the first case** (accelerating to 6 m/s): \(0.2 \, \text{m/s}^2\)
- **Acceleration during the second case** (decelerating to 4 m/s): \(-0.4 \, \text{m/s}^2\) (indicating retardation)