An object is verically thrown upwards. The the dislacement-time graph for the motion is as shown in .

Options

A. .
B. .
C. .
D. .

Explanation

To solve the problem of determining the correct displacement-time graph for an object thrown vertically upwards, we can follow these steps:

### Step 1: Understand the Motion
When an object is thrown vertically upwards, it moves against the force of gravity. Initially, it has a certain velocity (u) and as it rises, its velocity decreases until it reaches the highest point where the velocity becomes zero.

### Step 2: Analyze the Displacement
The displacement of the object can be described by the equation:
\[ s = ut - \frac{1}{2}gt^2 \]
where:
- \( s \) is the displacement,
- \( u \) is the initial velocity,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( t \) is the time.

### Step 3: Identify the Motion Phases
1. **Going Up (O to A)**: The object moves upwards, and the displacement increases. The velocity decreases until it reaches zero at the highest point (A).
2. **Coming Down (A to B)**: After reaching the highest point, the object starts to descend. The displacement decreases initially but then increases again as it falls back down.

### Step 4: Graphical Representation
- During the upward motion (O to A), the displacement increases and the graph will be a curve that rises and flattens out as it approaches the peak (A).
- At the peak (A), the slope of the graph (which represents velocity) becomes zero.
- During the downward motion (A to B), the displacement decreases initially and then increases again as the object falls back down, resulting in a curve that rises again.

### Step 5: Determine the Correct Option
From the analysis, the displacement-time graph will show:
- A curve that rises steeply at first (indicating increasing displacement as the object moves up).
- A flattening out at the peak (indicating the moment the object stops rising).
- A curve that descends and then rises again as the object falls back down.

Given the options, the correct displacement-time graph will be the one that matches this description, which is option B.

### Final Answer
The correct option for the displacement-time graph of an object thrown vertically upwards is **Option B**.

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