An athelete takes 2.0 s to reach his maximum speed of 18.0 km/h. What is the magnitude of his average acceleration?

Explanation

To find the magnitude of the athlete's average acceleration, we can follow these steps:

### Step 1: Identify the given values
- Final velocity (v) = 18.0 km/h
- Initial velocity (u) = 0 (the athlete starts from rest)
- Time taken (t) = 2.0 s

### Step 2: Convert the final velocity from km/h to m/s
To convert kilometers per hour to meters per second, we use the conversion factor:
\[ 1 \text{ km/h} = \frac{5}{18} \text{ m/s} \]
Thus, we convert 18.0 km/h:
\[ v = 18.0 \text{ km/h} \times \frac{5}{18} = 5.0 \text{ m/s} \]

### Step 3: Use the formula for average acceleration
The formula for average acceleration (a) is given by:
\[ a = \frac{v - u}{t} \]
Substituting the known values:
\[ a = \frac{5.0 \text{ m/s} - 0 \text{ m/s}}{2.0 \text{ s}} \]

### Step 4: Calculate the average acceleration
\[ a = \frac{5.0 \text{ m/s}}{2.0 \text{ s}} = 2.5 \text{ m/s}^2 \]

### Final Answer
The magnitude of the athlete's average acceleration is **2.5 m/s²**.

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