What is the magnitude of the average acceleration of a skier who, starting from rest, reaches a speed of 8.0 m/s when going down a slope for 5.0 s ?

Options

A. `0.85m//s^(2)`
B. `1.1 m//s^(2)`
C. `1.6 m//s^(2)`
D. `1.9 m//s^(2)`

Answer

To find the magnitude of the average acceleration of the skier, we can use the formula for average acceleration:

\[ a_{avg} = \frac{V - u}{t} \]

where:
- \( a_{avg} \) is the average acceleration,
- \( V \) is the final velocity,
- \( u \) is the initial velocity,
- \( t \) is the time taken.

### Step-by-Step Solution:

1. **Identify the initial velocity (u)**:
The skier starts from rest, so the initial velocity \( u = 0 \, \text{m/s} \).

2. **Identify the final velocity (V)**:
The final velocity after skiing down the slope is given as \( V = 8.0 \, \text{m/s} \).

3. **Identify the time taken (t)**:
The time taken to reach this final speed is \( t = 5.0 \, \text{s} \).

4. **Substitute the values into the acceleration formula**:
Now, we can substitute the values into the average acceleration formula:
\[ a_{avg} = \frac{V - u}{t} = \frac{8.0 \, \text{m/s} - 0 \, \text{m/s}}{5.0 \, \text{s}} \]

5. **Calculate the average acceleration**:
\[ a_{avg} = \frac{8.0 \, \text{m/s}}{5.0 \, \text{s}} = 1.6 \, \text{m/s}^2 \]

6. **State the final answer**:
The magnitude of the average acceleration of the skier is \( 1.6 \, \text{m/s}^2 \).