Position - time graph for motion with negative acceleration is

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Answer

To draw the position-time graph for motion with negative acceleration, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Negative Acceleration**:
- Negative acceleration (deceleration) means that the object is slowing down. This implies that the velocity of the object is decreasing over time.

2. **Equation of Motion**:
- The equation of motion for an object under constant acceleration is given by:
\[ x = ut + \frac{1}{2}at^2 \]
- For negative acceleration, we can express it as:
\[ x = ut - \frac{1}{2}|a|t^2 \]
- Here, \(u\) is the initial velocity, \(a\) is the magnitude of acceleration, and \(t\) is time.

3. **Identify the Shape of the Graph**:
- The term \(-\frac{1}{2}|a|t^2\) indicates that the graph will be a downward-opening parabola because the coefficient of \(t^2\) is negative.

4. **Plotting the Graph**:
- On the vertical axis (y-axis), we will plot the position \(x\) (in meters).
- On the horizontal axis (x-axis), we will plot time \(t\) (in seconds).
- At \(t = 0\), the position \(x\) will be equal to the initial position (which we can assume as the origin for simplicity).

5. **Drawing the Downward Parabola**:
- Starting from the origin (0,0), the graph will rise initially (if \(u > 0\)), reaching a maximum point (the vertex of the parabola) where the velocity becomes zero.
- After reaching the maximum height, the graph will curve downwards, indicating that the object is returning to the ground (or moving back towards the starting point).

6. **Labeling Important Points**:
- The highest point of the graph (the vertex) represents the maximum displacement where the velocity is zero.
- The point where the graph intersects the time axis again represents when the object returns to the starting position.

### Final Graph:
- The final graph will be a downward-opening parabola starting from the origin, peaking at a certain point, and then descending back towards the time axis.