Which of the quantity, velocity or acceleration determines the direction of motion ?

Explanation

To determine which quantity, velocity or acceleration, determines the direction of motion, we can analyze the definitions and roles of both quantities.

### Step-by-Step Solution:

1. **Define Velocity**:
- Velocity (v) is defined as the rate of change of displacement (s) with respect to time (t). Mathematically, it is expressed as:
\[ v = \frac{ds}{dt} \]
- This means that velocity has both magnitude and direction, indicating how fast an object is moving and in which direction.

2. **Define Acceleration**:
- Acceleration (a) is defined as the rate of change of velocity (v) with respect to time (t). It can be expressed as:
\[ a = \frac{dv}{dt} \]
- Acceleration also has both magnitude and direction, but it specifically describes how the velocity of an object is changing over time.

3. **Direction of Motion**:
- The direction of motion of an object is determined by the direction of its displacement. Displacement is a vector quantity that indicates the change in position of an object.
- Since velocity is directly related to displacement, the direction of the velocity vector indicates the direction in which the object is moving.

4. **Role of Acceleration**:
- While acceleration can change the velocity of an object, it does not directly indicate the direction of motion. Instead, it indicates how the velocity is changing, which may involve changing the direction of motion.
- For example, if an object is moving in a straight line and experiences acceleration, the acceleration will affect the speed and possibly the direction of the object, but the current direction of motion is still given by the velocity.

5. **Conclusion**:
- Therefore, the quantity that determines the direction of motion is **velocity**. It provides the direction of displacement, which is essential for understanding how and where an object is moving.

### Final Answer:
**Velocity determines the direction of motion.**

---