If velocity v varies with time t as `v=2t^(2)`, then the plot between v and `t^(2)` will be given as :

Options

A.
B.
C.
D.

Answer

To solve the problem of plotting the relationship between velocity \( v \) and \( t^2 \) given the equation \( v = 2t^2 \), we can follow these steps:

### Step 1: Identify the relationship
The equation given is \( v = 2t^2 \). This indicates that velocity \( v \) is directly proportional to the square of time \( t^2 \).

### Step 2: Rearrange the equation
We can express the equation in a form that highlights the linear relationship:
\[ v = 2(t^2) \]
This shows that \( v \) is a linear function of \( t^2 \) with a slope of 2.

### Step 3: Determine the characteristics of the graph
Since \( v \) is directly proportional to \( t^2 \), the graph of \( v \) versus \( t^2 \) will be a straight line.

### Step 4: Identify the intercept
The equation \( v = 2t^2 \) has no constant term, which means the line will pass through the origin (0,0).

### Step 5: Determine the slope
The slope of the line is 2, which indicates that for every unit increase in \( t^2 \), \( v \) increases by 2 units.

### Step 6: Sketch the graph
- Draw the coordinate axes with \( v \) on the vertical axis and \( t^2 \) on the horizontal axis.
- Start from the origin (0,0).
- Draw a straight line with a slope of 2. This means for every 1 unit increase in \( t^2 \), \( v \) increases by 2 units.

### Final Graph
The graph will be a straight line passing through the origin with a slope of 2.

---