https://file.aiquickdraw.com/mathbot/file/1726450561878i5my3cez.jpg

The graph in  (Figure 1) shows the velocity v
 of a sports car as a function of time t
. Use the graph to answer the following questions.Find the maximum acceleration  amax
  of the car.
Express your answer in meters per second per second to the nearest integer.

To determine the maximum acceleration \(a_{\text{max}}\) from the velocity-time graph, we need to find the region where the slope of the velocity curve is steepest. The acceleration is given by the rate of change of velocity with respect to time:

\[
a = \frac{\Delta v}{\Delta t}
\]

Let's analyze the graph step by step:

1. **Initial Region (0 to 2 seconds)**: The velocity increases from 0 m/s to 60 m/s in 2 seconds. The acceleration during this time is:

\[
a = \frac{60 \, \text{m/s} - 0 \, \text{m/s}}{2 \, \text{s} - 0 \, \text{s}} = \frac{60}{2} = 30 \, \text{m/s}^2
\]

2. **Middle Region (2 to 6 seconds)**: The velocity remains constant at 60 m/s, so the acceleration is 0 m/s².

3. **Final Region (6 to 9 seconds)**: The velocity decreases from 60 m/s to 0 m/s in 3 seconds. The acceleration during this phase is:

\[
a = \frac{0 \, \text{m/s} - 60 \, \text{m/s}}{9 \, \text{s} - 6 \, \text{s}} = \frac{-60}{3} = -20 \, \text{m/s}^2
\]

The maximum acceleration occurs in the initial region, where the slope is steepest. Therefore, the maximum acceleration \(a_{\text{max}}\) is:

\[
\boxed{30 \, \text{m/s}^2}
\]

Would you like more details, or do you have any questions?

Here are 5 related questions for further exploration:

1. What is the maximum deceleration of the car based on the graph?
2. How much distance did the car cover during the first 2 seconds?
3. What was the total distance traveled by the car during the 9-second period?
4. Can we calculate the average velocity of the car over the 9 seconds?
5. How would the graph change if the car experienced uniform acceleration throughout?

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

The graph in (Figure 1) shows the velocity v of a sports car as a function of time t. Use the graph to answer the following questions. Find the maximum acceleration amax of the car. Express your answer in meters per second per second to the nearest integer.

Learn how to find the maximum acceleration of a sports car using a velocity-time graph. This problem involves kinematics concepts, the formula a = Δv / Δt, and interpreting the slope of the graph. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation