If the velocity of a body does not change with time, its acceleraton is

Options

A. zero
B. infinite
C. unity
D. none of these

Answer

To solve the question, "If the velocity of a body does not change with time, its acceleration is?", we can follow these steps:

### Step 1: Understand the definition of acceleration
Acceleration is defined as the rate of change of velocity with respect to time. Mathematically, it is expressed as:
\[ a = \frac{dv}{dt} \]
where \( a \) is acceleration, \( dv \) is the change in velocity, and \( dt \) is the change in time.

**Hint:** Recall that acceleration measures how quickly velocity changes over time.

### Step 2: Analyze the condition given in the question
The question states that the velocity of the body does not change with time. This means that the velocity is constant.

**Hint:** Think about what it means for velocity to be constant. Does it change or remain the same?

### Step 3: Apply the definition of acceleration
Since the velocity is constant, the change in velocity (\( dv \)) is zero. Therefore, we can substitute this into the acceleration formula:
\[ a = \frac{dv}{dt} = \frac{0}{dt} \]

**Hint:** Consider what happens when the numerator of a fraction is zero.

### Step 4: Simplify the expression
Since \( dv = 0 \), we have:
\[ a = 0 \]

**Hint:** Remember that if there is no change in velocity, the acceleration must also be zero.

### Step 5: Conclusion
Thus, if the velocity of a body does not change with time, its acceleration is:
\[ \text{Acceleration} = 0 \]

**Final Answer:** The acceleration is 0.