A car starts from erest accelerates uniform by for 4 second and then moves with uniform velocity which of the x-t graph represent th motion of the car:-

Explanation

To solve the problem of determining which x-t graph represents the motion of a car that starts from rest, accelerates uniformly for 4 seconds, and then moves with uniform velocity, we can follow these steps:

### Step 1: Understand the Motion Phases
The car has two distinct phases of motion:
1. **Acceleration Phase**: The car accelerates uniformly from rest for 4 seconds.
2. **Constant Velocity Phase**: After 4 seconds, the car moves with a constant velocity.

### Step 2: Analyze the Acceleration Phase
During the first phase (0 to 4 seconds):
- The car starts from rest, which means its initial velocity (u) is 0.
- It accelerates uniformly, so we can denote the acceleration as 'a'.
- The displacement (x) during this phase can be calculated using the equation of motion:
\[ x = ut + \frac{1}{2} a t^2 \]
Since \( u = 0 \):
\[ x = \frac{1}{2} a t^2 \]
This equation represents a parabolic curve on the x-t graph, starting from the origin (0,0).

### Step 3: Determine the Velocity After 4 Seconds
At the end of the acceleration phase (t = 4 seconds), we can find the final velocity (v) using:
\[ v = u + at \]
Substituting \( u = 0 \):
\[ v = a \cdot 4 = 4a \]
This velocity will remain constant during the second phase of motion.

### Step 4: Analyze the Constant Velocity Phase
During the second phase (after 4 seconds):
- The car moves with a constant velocity of \( 4a \).
- The displacement can be expressed as:
\[ x = x_0 + vt \]
where \( x_0 \) is the displacement at \( t = 4 \) seconds, and \( v = 4a \).

### Step 5: Combine Both Phases on the x-t Graph
1. From \( t = 0 \) to \( t = 4 \): The graph will be a parabolic curve starting from the origin (0,0).
2. From \( t = 4 \) onwards: The graph will be a straight line with a positive slope, representing constant velocity.

### Conclusion
The x-t graph will start at the origin, curve upwards (parabola) for the first 4 seconds, and then transition into a straight line with a constant slope after 4 seconds.