Which one is a vector quantity?

Options

A. Work
B. momentum
C. time
D. Speed

Explanation

To determine which one is a vector quantity among the given options, we will analyze each option step by step.

### Step 1: Analyze Work
- **Definition**: Work (W) is defined as the dot product of force (F) and displacement (S), given by the formula:
\[ W = F \cdot S \cos(\theta) \]
- **Nature**: Since work is derived from the dot product of two vectors (force and displacement), it results in a scalar quantity. Therefore, work is not a vector quantity.

### Step 2: Analyze Momentum
- **Definition**: Momentum (P) is defined as the product of mass (m) and velocity (v):
\[ P = m \cdot v \]
- **Nature**: Since velocity is a vector quantity (having both magnitude and direction), and mass is a scalar, the product of mass and velocity results in a vector quantity. Therefore, momentum is a vector quantity.

### Step 3: Analyze Time
- **Definition**: Time is a measure of the duration of events.
- **Nature**: Time is a scalar quantity as it only has magnitude and does not have any direction. Therefore, time is not a vector quantity.

### Step 4: Analyze Speed
- **Definition**: Speed is defined as the distance traveled per unit time:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
- **Nature**: Both distance and time are scalar quantities (distance has magnitude only, and time has magnitude only). Therefore, speed is also a scalar quantity and not a vector quantity.

### Conclusion
After analyzing all the options:
- Work: Scalar Quantity
- Momentum: Vector Quantity
- Time: Scalar Quantity
- Speed: Scalar Quantity

Thus, the correct answer is that **momentum is the vector quantity**.

### Final Answer
The vector quantity among the options is **momentum**.

---