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
- Maximum speed (V_max) = 18.0 km/h
- Time taken (t) = 2.0 s
- Initial speed (U) = 0 m/s (since the athlete starts from rest)

### Step 2: Convert the maximum speed from km/h to m/s
To convert kilometers per hour to meters per second, we use the conversion factor:
\[ 1 \text{ km/h} = \frac{5}{18} \text{ m/s} \]
So, we calculate:
\[ V_{\text{max}} = 18.0 \text{ km/h} \times \frac{5}{18} \text{ m/s per km/h} \]
\[ V_{\text{max}} = 18.0 \times \frac{5}{18} = 5.0 \text{ m/s} \]

### Step 3: Use the formula for average acceleration
The formula for average acceleration (A_avg) is given by:
\[ A_{\text{avg}} = \frac{V - U}{t} \]
Where:
- V = final velocity (V_max)
- U = initial velocity
- t = time taken

Substituting the values we have:
\[ A_{\text{avg}} = \frac{5.0 \text{ m/s} - 0 \text{ m/s}}{2.0 \text{ s}} \]
\[ A_{\text{avg}} = \frac{5.0 \text{ m/s}}{2.0 \text{ s}} \]
\[ A_{\text{avg}} = 2.5 \text{ m/s}^2 \]

### Step 4: State the final answer
The magnitude of the athlete's average acceleration is **2.5 m/s²**.

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