https://file.aiquickdraw.com/mathbot/file/1725072695069v9lf3xfl.jpg

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

Quiz2Figure2 - Velocity vs Time.jpg

Group of answer choices

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

The car moves in the same direction from time a to time c

The car's acceleration from time a to time b is positive.

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

At time b, the car velocity is zero.

The car's average acceleration between time a and time c is negative.

The car's average acceleration between time a and time c is zero.

The car's speed at time instant a is the same as that at instant c.

The car's acceleration from time b to time c is negative.

The car's average acceleration between time a and time c is positive.

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

### Graph Analysis:
1. **Intervals**:
   - **From \( a \) to \( b \)**: Velocity increases linearly, suggesting positive acceleration.
   - **At \( b \)**: The velocity reaches its peak and then decreases, suggesting this point might represent a maximum velocity.
   - **From \( b \) to \( c \)**: Velocity decreases linearly, suggesting negative acceleration.

2. **Key Observations**:
   - At time \( c \), the velocity returns to zero, similar to time \( a \).

### Evaluating the Statements:
1. **"At time c, the car has returned to the location where it started at time a."**
   - This statement is **correct** because the area under the velocity-time graph (which represents displacement) from \( a \) to \( c \) sums to zero, implying the car has returned to the starting point.

2. **"The car moves in the same direction from time a to time c."**
   - This statement is **incorrect** because the velocity changes direction at point \( b \).

3. **"The car's acceleration from time a to time b is positive."**
   - This statement is **correct** because the slope from \( a \) to \( b \) is positive.

4. **"At time b, the car reverses its direction of motion."**
   - This statement is **incorrect** because at point \( b \), the car does not reverse direction but reaches its maximum velocity before slowing down.

5. **"At time b, the car velocity is zero."**
   - This statement is **incorrect** because velocity at \( b \) is at its maximum, not zero.

6. **"The car's average acceleration between time a and time c is negative."**
   - This statement is **correct** because the overall change in velocity from \( a \) to \( c \) is negative.

7. **"The car's average acceleration between time a and time c is zero."**
   - This statement is **incorrect** because the average acceleration is negative.

8. **"The car's speed at time instant a is the same as that at instant c."**
   - This statement is **correct** because both instants show zero velocity.

9. **"The car's acceleration from time b to time c is negative."**
   - This statement is **correct** because the slope of the graph is negative from \( b \) to \( c \).

10. **"The car's average acceleration between time a and time c is positive."**
    - This statement is **incorrect** because the average acceleration is negative.

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

1. How can you calculate the displacement of the car using the velocity vs. time graph?
2. What does the area under a velocity vs. time graph represent in kinematics?
3. How can you determine the average speed of the car between two points on the graph?
4. What is the significance of the slope in a velocity vs. time graph?
5. How can we find the exact time when the car changes direction?

**Tip:** In a velocity vs. time graph, the area under the curve gives the displacement, and the slope gives the acceleration.

Explore the analysis of car motion using a velocity vs. time graph. Understand concepts like acceleration, velocity changes, and direction reversals. Detailed solutions to problems based on velocity-time graphs.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation