A student pushes a box whose mass is 50 kg for a distance of 2.0 m over a smooth horizontal surface. She exerts a constant force of 100 N in a particular direction. If the box starts from rest then find its final velocity.

Options

A. 2 m/s
B. 4 m/s
C. 2.83 m/s
D. 1.41 m/s

Answer

To find the final velocity of the box after being pushed by the student, we can follow these steps:

### Step 1: Identify the known values
- Mass of the box (m) = 50 kg
- Force applied (F) = 100 N
- Distance moved (s) = 2.0 m
- Initial velocity (u) = 0 m/s (since the box starts from rest)

### Step 2: Calculate the acceleration
Using Newton's second law of motion, we can find the acceleration (a) using the formula:
\[ F = m \cdot a \]
Rearranging this gives:
\[ a = \frac{F}{m} \]
Substituting the known values:
\[ a = \frac{100 \, \text{N}}{50 \, \text{kg}} = 2 \, \text{m/s}^2 \]

### Step 3: Use the equation of motion to find the final velocity
We can use the following equation of motion:
\[ v^2 = u^2 + 2as \]
Substituting the known values:
\[ v^2 = 0^2 + 2 \cdot (2 \, \text{m/s}^2) \cdot (2.0 \, \text{m}) \]
Calculating this gives:
\[ v^2 = 0 + 8 = 8 \]
Taking the square root to find v:
\[ v = \sqrt{8} = 2\sqrt{2} \approx 2.83 \, \text{m/s} \]

### Final Answer
The final velocity of the box after being pushed is approximately **2.83 m/s**.

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