How long will it take a force of 10 N to stop a mass of 2.5 kg which is moving at 20 m/s?

Answer

To solve the problem of how long it will take a force of 10 N to stop a mass of 2.5 kg moving at 20 m/s, we can follow these steps:

### Step 1: Identify the given values
- Mass (m) = 2.5 kg
- Initial velocity (u) = 20 m/s
- Force (F) = 10 N

### Step 2: Calculate the acceleration (or retardation)
Using Newton's second law of motion, we can find the acceleration produced by the force:
\[ F = m \cdot a \]
Rearranging this gives us:
\[ a = \frac{F}{m} \]
Substituting the values:
\[ a = \frac{10 \, \text{N}}{2.5 \, \text{kg}} = 4 \, \text{m/s}^2 \]
Since the force is acting in the opposite direction to the motion (to stop the object), the acceleration will be negative:
\[ a = -4 \, \text{m/s}^2 \]

### Step 3: Use the first equation of motion
We will use the first equation of motion to find the time taken to stop:
\[ v = u + at \]
Where:
- v = final velocity = 0 m/s (since the object stops)
- u = initial velocity = 20 m/s
- a = acceleration = -4 m/s²

Substituting the known values:
\[ 0 = 20 + (-4)t \]
This simplifies to:
\[ 0 = 20 - 4t \]
Rearranging gives:
\[ 4t = 20 \]
Now, solving for t:
\[ t = \frac{20}{4} = 5 \, \text{seconds} \]

### Conclusion
The time taken to stop the mass of 2.5 kg moving at 20 m/s with a force of 10 N is **5 seconds**.

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