An object is moving with uniform acceleration a. Its initial velocity is u and after time t its velocity is v. The equation of its motion is v = u + at. The velocity (along y-axis) time (along x-axis) graph shall be a straight line

Options

A. passing through origin
B. with x-intercept u
C. with y-intercept u
D. with slope u

Explanation

To solve the problem step by step, we will analyze the motion of an object with uniform acceleration and derive the corresponding velocity-time graph.

### Step 1: Understand the given equation
The equation of motion for an object moving with uniform acceleration is given by:
\[ v = u + at \]
where:
- \( v \) = final velocity
- \( u \) = initial velocity
- \( a \) = acceleration
- \( t \) = time

### Step 2: Identify the variables for the graph
In this scenario, we will plot:
- The y-axis will represent the velocity \( v \).
- The x-axis will represent the time \( t \).

### Step 3: Rearrange the equation
We can rearrange the equation \( v = u + at \) to fit the form of a straight line equation \( y = mx + c \):
- Here, \( v \) (velocity) is the dependent variable (y-axis).
- \( t \) (time) is the independent variable (x-axis).
- The equation can be rewritten as:
\[ v = at + u \]
This shows that:
- The slope \( m \) of the line is equal to the acceleration \( a \).
- The y-intercept \( c \) is equal to the initial velocity \( u \).

### Step 4: Graph the equation
Now, we can sketch the graph:
- Start by plotting the y-intercept \( u \) on the y-axis.
- Since the slope is \( a \), for every unit increase in \( t \), \( v \) increases by \( a \).
- Draw a straight line starting from the point \( (0, u) \) and extending upwards with a slope of \( a \).

### Step 5: Analyze the graph
The graph will be a straight line:
- The slope of the line represents the acceleration \( a \).
- The point where the line intersects the y-axis represents the initial velocity \( u \).

### Conclusion
Thus, the velocity-time graph for an object moving with uniform acceleration is a straight line with:
- Slope = \( a \) (acceleration)
- Y-intercept = \( u \) (initial velocity)