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

Answer

To solve the problem of determining the directions of velocity and acceleration of a lift that is ascending with decreasing speed, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Motion of the Lift**:
- The lift is described as "ascending," which means it is moving upward.

2. **Determine the Direction of Velocity**:
- Since the lift is moving upward, the direction of its velocity is also upward.
- In physics, we often consider upward motion as positive. Therefore, we can say:
- **Velocity (v)**: Upward direction (positive).

3. **Analyze the Speed of the Lift**:
- The problem states that the lift is ascending with "decreasing speed." This means that although the lift is moving upward, its speed is getting less over time.

4. **Determine the Rate of Change of Velocity**:
- The phrase "decreasing speed" indicates that the velocity of the lift is decreasing. In mathematical terms, this means that the derivative of velocity with respect to time (dv/dt) is negative.
- Therefore, we conclude:
- **Acceleration (a)**: Since the speed is decreasing, the acceleration must be in the opposite direction to the velocity. In this case, it is downward.

5. **Summarize the Directions**:
- **Direction of Velocity**: Upward (positive).
- **Direction of Acceleration**: Downward (negative).

### Final Answer:
- The direction of velocity of the lift is upward, while the direction of acceleration is downward.