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A car moves along s straight line. The figure shows the car's Position vs. Time graph. Which of the following statements is (are) correct?

Group of answer choices

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

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

At time b, the car velocity is zero.

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

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.

Understand car motion with a position vs. time graph analysis. Learn which statements are correct based on the graph provided. Explore concepts like velocity, direction reversal, and graph interpretation.

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