When the distance an object travels is directly proportional to the length of time , it is said to travel with

Options

A. zero velocity
B. constant speed
C. constant acceleration
D. uniform velocity

Answer

To solve the question, we need to analyze the relationship between distance traveled and time taken. The question states that the distance an object travels is directly proportional to the length of time. Let's break this down step by step.

### Step-by-Step Solution:

1. **Understanding Direct Proportionality**:
- When we say that distance (d) is directly proportional to time (t), we can express this relationship mathematically as:
\[ d \propto t \]
- This means that if time increases, distance increases at a constant rate.

2. **Introducing a Constant**:
- To convert the proportionality into an equation, we introduce a constant of proportionality (k):
\[ d = k \cdot t \]
- Here, \( k \) represents the speed of the object.

3. **Identifying the Type of Motion**:
- The equation \( d = k \cdot t \) indicates that the distance traveled is a linear function of time. This is characteristic of uniform motion.
- In this case, the object travels equal distances in equal intervals of time, which means it is moving at a constant speed.

4. **Understanding Velocity**:
- Velocity is defined as the rate of change of distance with respect to time. Mathematically, this is expressed as:
\[ v = \frac{d}{dt} \]
- Since \( d = k \cdot t \), we can differentiate this with respect to time:
\[ v = \frac{d}{dt} (k \cdot t) = k \]
- This shows that the velocity (v) is constant and equal to the constant \( k \).

5. **Conclusion**:
- Since the distance traveled is directly proportional to time and the velocity remains constant, we conclude that the object is traveling with **constant speed**.

### Final Answer:
The object is said to travel with **constant speed**.

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