Based on the position vs. time graph provided, let's analyze the car's motion to determine which statements are correct.

Graph Analysis:

1. Intervals:

   • From $a$ to $b$: Position increases linearly, suggesting the car is moving forward with constant speed.
   • At $b$: The position reaches its maximum value, indicating a momentary stop as the car changes direction.
   • From $b$ to $c$: Position decreases linearly, suggesting the car is moving back towards its starting point with constant speed.

2. Key Observations:

   • At point $b$, the slope of the position vs. time graph is zero, indicating zero velocity.
   • At time $c$, the car's position is back to the initial position at time $a$.

Evaluating the Statements:

1. "At time b, the car reverses its direction of motion."

   • This statement is correct because at time $b$, the car stops and changes direction, as indicated by the peak in the position graph.

2. "The car's speed is zero at time instants a and c."

   • This statement is incorrect because the car’s speed is not zero at $a$ and $c$; at both times, the car is moving since the graph shows a non-zero slope.

3. "At time b, the car velocity is zero."

   • This statement is correct because the slope of the graph at time $b$ is zero, indicating zero velocity.

4. "At time c, the car has returned to the location where it started at time a."

   • This statement is correct because the position at $c$ is the same as at $a$.

Would you like any further details or explanations? Here are some related questions:

1. How can you determine the velocity of the car at any point from the position vs. time graph?
2. What does the slope of a position vs. time graph represent in kinematics?
3. How can you calculate the total distance traveled by the car from time $a$ to time $c$?
4. What is the significance of a peak in a position vs. time graph?
5. How would the graph look if the car accelerated from time $a$ to $b$ instead of moving at a constant speed?

Tip: In a position vs. time graph, the slope of the graph represents the velocity of the object. A zero slope indicates zero velocity at that instant.