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 acceleration
B. unifrom retardation
C. non-uniform acceleration
D. zero acceleration

Explanation

To determine the type of motion a body is undergoing when its velocity depends on time according to the equation \( v = 20 + 0.1 t^2 \), we will follow these steps:

### Step 1: Identify the given equation
The velocity of the body is given by the equation:
\[ v = 20 + 0.1 t^2 \]

### Step 2: Differentiate the velocity equation to find acceleration
Acceleration \( a \) is defined as the rate of change of velocity with respect to time. Therefore, we differentiate the velocity equation with respect to time \( t \):
\[ a = \frac{dv}{dt} \]

Calculating the derivative:
\[ a = \frac{d}{dt}(20 + 0.1 t^2) = 0 + 0.2 t = 0.2 t \]

### Step 3: Analyze the acceleration
From the differentiation, we find that:
\[ a = 0.2 t \]
This indicates that the acceleration depends on time \( t \).

### Step 4: Determine the nature of acceleration
- The acceleration \( a = 0.2 t \) is positive since \( 0.2 \) is a positive constant and \( t \) is always non-negative (assuming \( t \geq 0 \)).
- However, the key point is that \( a \) is not constant; it varies with time. As time increases, acceleration also increases.

### Step 5: Classify the type of motion
Since the acceleration is positive and varies with time, the body is undergoing **non-uniform acceleration**.

### Conclusion
The body is undergoing non-uniform acceleration as the acceleration is not constant and increases with time.

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