In a race a 70 kg sprinter covers first 20 m in 5.0 s, starting from rest and accelerating uniformly. What is the average power the sprinter generate during the 5.0 s interval?

Options

A. 1120 W
B. 112 W
C. 224 W
D. 448 W

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Identify the Given Data
- Mass of the sprinter (m) = 70 kg
- Distance covered (s) = 20 m
- Time taken (t) = 5.0 s
- Initial velocity (u) = 0 m/s (starting from rest)

### Step 2: Use the Equation of Motion to Find Acceleration
We can use the second equation of motion, which is:
\[ s = ut + \frac{1}{2} a t^2 \]
Substituting the known values:
\[ 20 = 0 \cdot 5 + \frac{1}{2} a (5)^2 \]
This simplifies to:
\[ 20 = \frac{1}{2} a \cdot 25 \]
\[ 20 = 12.5a \]
Now, solving for \(a\):
\[ a = \frac{20}{12.5} = 1.6 \, \text{m/s}^2 \]

### Step 3: Calculate the Work Done
The work done (W) can be calculated using the formula:
\[ W = F \cdot s \]
Where the force \(F\) is given by:
\[ F = m \cdot a \]
Substituting the values:
\[ F = 70 \cdot 1.6 = 112 \, \text{N} \]
Now, substituting \(F\) into the work done equation:
\[ W = 112 \cdot 20 = 2240 \, \text{J} \]

### Step 4: Calculate the Average Power
The average power (P) is given by the formula:
\[ P = \frac{W}{t} \]
Substituting the values:
\[ P = \frac{2240}{5} = 448 \, \text{W} \]

### Conclusion
The average power generated by the sprinter during the 5.0 s interval is **448 Watts**.

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