When the velocity is greater than​ 0, the object is moving to the right. Examine the problem statement to determine the interval over which the function is defined

To determine the interval over which a function is defined and where the object is moving to the right (i.e., when velocity \( v(t) > 0 \)), we need the following information:

1. The function representing the velocity of the object, usually \( v(t) \), where \( t \) is time.
2. Any given conditions or restrictions on the domain of the velocity function.

### General Steps:
1. **Identify the velocity function \( v(t) \)**: The object is moving to the right whenever the velocity \( v(t) > 0 \). If the velocity function is given or can be derived, determine the points where \( v(t) = 0 \) or where \( v(t) \) changes sign.
   
2. **Solve for critical points**: Find the values of \( t \) where \( v(t) = 0 \), as these are the points where the object could change direction (i.e., where the velocity could change from positive to negative or vice versa).

3. **Determine sign of \( v(t) \)**: Analyze the intervals around these critical points by testing values of \( t \) in each interval to see whether \( v(t) > 0 \) (object moving to the right) or \( v(t) < 0 \) (object moving to the left).

4. **Domain of the function**: The problem may provide an explicit domain (e.g., "the velocity function is defined for \( t \geq 0 \)"). Otherwise, check the natural domain of the function, which is typically the set of all \( t \)-values for which the function makes sense (no division by zero or square roots of negative numbers).

5. **Interval where the velocity is greater than 0**: The object moves to the right on intervals where \( v(t) > 0 \). These intervals can be extracted after determining where \( v(t) \) is positive.

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Would you like to provide the specific velocity function or any additional details about the problem so I can help you find the intervals where the object moves to the right?

### 5 Related Questions:
1. How do we find the points where an object changes direction?
2. What if the velocity function is a quadratic or cubic equation—how does that affect the interval analysis?
3. How do you determine whether an object is accelerating or decelerating based on velocity?
4. Can an object have zero velocity while still moving in the future?
5. What happens to the object's motion if the velocity is negative?

**Tip**: When solving for intervals where a function is positive or negative, remember to check the behavior of the function around critical points carefully!

When the velocity is greater than 0, the object is moving to the right. Examine the problem statement to determine the interval over which the function is defined.

Analyze how an object moves based on its velocity function by determining intervals where the velocity is positive. Learn key concepts such as critical points and sign analysis in this calculus-based problem, suitable for students in Grades 11-12 or early college.

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