A force of 75 N is applied to a block of mass 25 kg, resting on a smooth horizontal surface. In how much time, the block will acquire a speed of 12 m/s?

Options

A. `1` sec
B. `2`sec
C. `4` sec
D. `8` sec

Explanation

To solve the problem, we will use Newton's second law of motion and the concept of momentum. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the Given Information
- Force (F) = 75 N
- Mass (m) = 25 kg
- Final speed (v) = 12 m/s
- Initial speed (u) = 0 m/s (since the block is at rest)

### Step 2: Calculate the Change in Momentum
Momentum (p) is defined as the product of mass and velocity.
- Initial momentum (p_initial) = m * u = 25 kg * 0 m/s = 0 kg·m/s
- Final momentum (p_final) = m * v = 25 kg * 12 m/s = 300 kg·m/s

Now, we can find the change in momentum (Δp):
\[ \Delta p = p_{final} - p_{initial} = 300 kg·m/s - 0 kg·m/s = 300 kg·m/s \]

### Step 3: Apply Newton's Second Law
According to Newton's second law:
\[ F = \frac{\Delta p}{\Delta t} \]
Where:
- F is the force applied
- Δp is the change in momentum
- Δt is the time taken

Rearranging the formula to find Δt:
\[ \Delta t = \frac{\Delta p}{F} \]

### Step 4: Substitute the Values
Now we can substitute the values we have:
\[ \Delta t = \frac{300 kg·m/s}{75 N} \]

### Step 5: Calculate Δt
Calculating the above expression:
\[ \Delta t = \frac{300}{75} = 4 \text{ seconds} \]

### Conclusion
The block will acquire a speed of 12 m/s in **4 seconds**.

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