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If the velocity of an object is increasi...

If the velocity of an object is increasing and changing at a uniform rate then the acceleration of the object is
`"(i) Positive (ii) Zero"`
`" (iii) Negative (iv) Not defined"`

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The correct Answer is:
To solve the problem, we need to analyze the relationship between velocity, acceleration, and how they change over time. ### Step-by-Step Solution: 1. **Understanding the Problem**: - We are given that the velocity of an object is increasing and changing at a uniform rate. 2. **Defining 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. 3. **Analyzing the Given Information**: - Since the velocity is increasing, we can say that \(dv > 0\) (the change in velocity is positive). - The phrase "changing at a uniform rate" implies that this change in velocity is consistent over time, meaning that \( \frac{dv}{dt} \) is constant. 4. **Determining the Sign of Acceleration**: - If \( \frac{dv}{dt} \) is constant and positive, then acceleration \(a\) must also be positive: \[ a = \frac{dv}{dt} > 0 \] 5. **Conclusion**: - Since the acceleration is positive, we can conclude that the correct answer to the question is: \[ \text{(i) Positive} \] ### Final Answer: The acceleration of the object is **Positive**. ---
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