"A lift is ascending with decreasing speed". What are the directions of velocity and acceleration of the lift at the given instant.

Explanation

To solve the problem, we need to analyze the situation of the lift that is ascending with decreasing speed.

### Step-by-step Solution:

1. **Identify the Direction of Velocity:**
- The lift is ascending, which means it is moving upwards. In physics, we often take upwards as the positive direction. Therefore, the velocity of the lift is directed upwards.
- **Direction of Velocity:** Positive y-direction (upward).

2. **Understand the Concept of Acceleration:**
- Acceleration is defined as the rate of change of velocity. It can be positive or negative depending on whether the velocity is increasing or decreasing.
- Since the lift is ascending with decreasing speed, this indicates that the velocity of the lift is getting smaller over time.

3. **Determine the Sign of Acceleration:**
- Because the speed of the lift is decreasing, the change in velocity (dv) is negative. Therefore, the acceleration (a) can be expressed as:
\[ a = \frac{dv}{dt} \]
Since dv is negative (the speed is decreasing), the acceleration will also be negative.
- **Direction of Acceleration:** Since acceleration is negative and acts in the opposite direction to the velocity, it will be directed downwards.

4. **Conclusion:**
- The direction of velocity of the lift is in the upward direction (positive y-direction).
- The direction of acceleration of the lift is in the downward direction.

### Final Answer:
- **Direction of Velocity:** Upward (positive y-direction)
- **Direction of Acceleration:** Downward