At t = 0 and u = 0, an object begins to be uniformly accelerated by a force of 40 N. The momentum of the body at t= 4 s is

Explanation

To solve the problem step by step, we will use the concepts of Newton's laws of motion and the relationship between force, momentum, and time.

### Step 1: Understand the Given Information
- Initial velocity (u) = 0 m/s (at t = 0)
- Force (F) = 40 N
- Time (t) = 4 s

### Step 2: Use Newton's Second Law
According to Newton's second law, force is equal to the rate of change of momentum:
\[ F = \frac{\Delta p}{\Delta t} \]
Where:
- \( \Delta p \) is the change in momentum
- \( \Delta t \) is the change in time

### Step 3: Express Change in Momentum
The change in momentum can be expressed as:
\[ \Delta p = p_f - p_i \]
Where:
- \( p_f \) is the final momentum
- \( p_i \) is the initial momentum

Given that the initial velocity is 0, the initial momentum \( p_i \) is:
\[ p_i = m \cdot u = m \cdot 0 = 0 \]

Thus, the change in momentum becomes:
\[ \Delta p = p_f - 0 = p_f \]

### Step 4: Substitute Values into the Equation
Now substituting into the equation of force:
\[ F = \frac{p_f}{t} \]
Rearranging gives:
\[ p_f = F \cdot t \]

### Step 5: Calculate Final Momentum
Substituting the values of force and time:
\[ p_f = 40 \, \text{N} \cdot 4 \, \text{s} = 160 \, \text{kg m/s} \]

### Final Answer
The momentum of the body at \( t = 4 \, \text{s} \) is:
\[ \boxed{160 \, \text{kg m/s}} \]

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