The linear momentum of a particle as a fuction of time 't' is given by , p = a +bt , where a and b are positive constants . What is the force acting on the particle ?

Options

A. a
B. b
C. ab
D. a+b

Answer

To find the force acting on the particle given its linear momentum as a function of time, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the given momentum function**:
The linear momentum \( p \) of the particle is given by the equation:
\[ p = a + bt \]
where \( a \) and \( b \) are positive constants and \( t \) is time.

2. **Recall the relationship between force and momentum**:
The force \( F \) acting on an object is defined as the rate of change of momentum with respect to time:
\[ F = \frac{dp}{dt} \]

3. **Differentiate the momentum function**:
To find the force, we need to differentiate the momentum function \( p \) with respect to time \( t \):
\[ \frac{dp}{dt} = \frac{d}{dt}(a + bt) \]
Since \( a \) is a constant, its derivative with respect to time is 0. The derivative of \( bt \) with respect to \( t \) is \( b \):
\[ \frac{dp}{dt} = 0 + b = b \]

4. **Substitute the derivative into the force equation**:
Now that we have the derivative of momentum, we can express the force:
\[ F = b \]

5. **Conclusion**:
Therefore, the force acting on the particle is:
\[ F = b \text{ Newtons} \]

### Final Answer:
The force acting on the particle is \( b \) Newtons.