The velocity of a body depends on time according to the equative `v = 20 + 0.1 t^(2)`. The body is undergoing

Options

A. Uniform retardation
B. Uniform acceleration
C. Non uniform acceleration
D. Zero acceleration

Answer

To solve the problem, we need to determine the nature of the acceleration of the body whose velocity is given by the equation \( v = 20 + 0.1 t^2 \).

### Step-by-Step Solution:

1. **Identify the given equation for velocity**:
\[ v = 20 + 0.1 t^2 \]
Here, \( v \) is the velocity of the body, and \( t \) is the time.

2. **Find the acceleration**:
Acceleration \( a \) is defined as the rate of change of velocity with respect to time, which can be expressed mathematically as:
\[ a = \frac{dv}{dt} \]
To find \( a \), we need to differentiate the velocity function \( v \) with respect to \( t \).

3. **Differentiate the velocity function**:
- The derivative of a constant (20) is 0.
- The derivative of \( 0.1 t^2 \) is \( 0.1 \cdot 2t = 0.2t \).

Therefore, the acceleration is:
\[ a = \frac{dv}{dt} = 0 + 0.2t = 0.2t \]

4. **Analyze the acceleration**:
The expression \( a = 0.2t \) indicates that acceleration is a function of time \( t \). This means that as time increases, the acceleration also increases.

5. **Determine the nature of acceleration**:
- Since the acceleration \( a = 0.2t \) changes with time, it is not constant.
- A constant acceleration would mean that \( a \) does not depend on \( t \), which is not the case here.

6. **Conclusion**:
The body is undergoing **non-uniform acceleration** because the acceleration depends on time and changes as time progresses.