An object of mass `100kg` is accelerated uniformly from a velocity of `5m//s` to `8m//s` in `6 s`. Calculate the initial and final momentum of the object. Also, find the magnitude of the force exerted on the object.

Explanation

To solve the problem step by step, we will calculate the initial and final momentum of the object, and then find the magnitude of the force exerted on it.

### Step 1: Calculate the Initial Momentum
The formula for momentum (p) is given by:
\[ p = m \times v \]
where:
- \( m \) is the mass of the object,
- \( v \) is the velocity of the object.

Given:
- Mass \( m = 100 \, \text{kg} \)
- Initial velocity \( u = 5 \, \text{m/s} \)

Now, substituting the values:
\[ p_{\text{initial}} = 100 \, \text{kg} \times 5 \, \text{m/s} = 500 \, \text{kg m/s} \]

### Step 2: Calculate the Final Momentum
Using the same formula for momentum:
Given:
- Final velocity \( v = 8 \, \text{m/s} \)

Now, substituting the values:
\[ p_{\text{final}} = 100 \, \text{kg} \times 8 \, \text{m/s} = 800 \, \text{kg m/s} \]

### Step 3: Calculate the Acceleration
To find the acceleration, we can use the formula:
\[ v = u + at \]
Rearranging gives:
\[ a = \frac{v - u}{t} \]

Given:
- \( v = 8 \, \text{m/s} \)
- \( u = 5 \, \text{m/s} \)
- \( t = 6 \, \text{s} \)

Now, substituting the values:
\[ a = \frac{8 \, \text{m/s} - 5 \, \text{m/s}}{6 \, \text{s}} = \frac{3 \, \text{m/s}}{6 \, \text{s}} = 0.5 \, \text{m/s}^2 \]

### Step 4: Calculate the Force
Using Newton's second law of motion:
\[ F = m \times a \]

Given:
- Mass \( m = 100 \, \text{kg} \)
- Acceleration \( a = 0.5 \, \text{m/s}^2 \)

Now, substituting the values:
\[ F = 100 \, \text{kg} \times 0.5 \, \text{m/s}^2 = 50 \, \text{N} \]

### Summary of Results
- Initial Momentum: \( 500 \, \text{kg m/s} \)
- Final Momentum: \( 800 \, \text{kg m/s} \)
- Magnitude of Force: \( 50 \, \text{N} \)

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