**Deceleration Required to Avoid Collision**

In order for the cyclist to avoid colliding with the wall, she needs to come to a stop before reaching it. This means that she must decrease her velocity from 15 m/s to 0 m/s. The deceleration required to achieve this depends on the distance between the cyclist and the wall, as well as the time available to stop.

**Using the Kinematic Equation**

To determine the required deceleration, we can use the following kinematic equation:

\[v^2 = u^2 + 2as\]

Where:
- \(v\) is the final velocity (0 m/s)
- \(u\) is the initial velocity (15 m/s)
- \(a\) is the acceleration (deceleration in this case)
- \(s\) is the distance traveled

**Rearranging the Equation**

Rearranging the equation, we get:

\[0 = (15)^2 + 2a(s)\]

\[0 = 225 + 2as\]

**Simplifying the Equation**

Since the cyclist wants to stop before reaching the wall, the distance traveled (\(s\)) is the distance to the wall. Therefore, we can rewrite the equation as:

\[0 = 225 + 2a(d)\]

Where:
- \(d\) is the distance to the wall

**Solving for Deceleration**

To find the required deceleration, we need to solve the equation for \(a\):

\[2a(d) = -225\]

\[a = \frac{-225}{2d}\]

The negative sign indicates that the deceleration is in the opposite direction of the initial velocity.

**Example Calculation**

Let's assume the distance to the wall is 10 meters. Plugging this value into the equation, we can calculate the required deceleration:

\[a = \frac{-225}{2(10)}\]

\[a = \frac{-225}{20}\]

\[a = -11.25 \, \text{m/s}^2\]

Therefore, in order to avoid colliding with the wall, the cyclist must have a deceleration of -11.25 m/s².

It's important to note that the negative sign indicates deceleration, which means the cyclist is slowing down.

Fine but what is the time? If there will be no time then it will not be possible to find the deceleration.