Math Problem Statement

What is the acceleration at 8 seconds

What is the acceleration at 8 seconds?

Solution

To determine the acceleration at 8 seconds, we need to analyze the velocity vs. time graph. Acceleration is the rate of change of velocity, so it can be found by calculating the slope of the velocity-time graph.

Let's break it down:

  1. At 8 seconds, the graph shows the velocity to be around -3 m/s.
  2. Between 6 and 9 seconds, the velocity changes from 0 m/s to -4 m/s.

The slope (acceleration) over this period is calculated by:

Acceleration=ΔvΔt=4096=43 m/s2=43 m/s2\text{Acceleration} = \frac{\Delta v}{\Delta t} = \frac{-4 - 0}{9 - 6} = \frac{-4}{3} \text{ m/s}^2 = -\frac{4}{3} \text{ m/s}^2

Thus, the acceleration at 8 seconds is:

43m/s2\boxed{-\frac{4}{3} \, \text{m/s}^2}

Would you like further details or explanations?

Here are 5 related questions:

  1. What is the total displacement during the 9-second interval?
  2. How would you calculate the average velocity over the entire interval?
  3. What is the object's position at 9 seconds if it started at 10 m?
  4. How would you describe the motion from 2 to 5 seconds?
  5. Can you determine the maximum acceleration in the graph?

Tip: Remember, in a velocity-time graph, the slope at any point gives the acceleration!

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Math Problem Analysis

Mathematical Concepts

Kinematics
Acceleration
Velocity-Time Graph

Formulas

Acceleration = (Change in velocity) / (Change in time)

Theorems

Slope of velocity-time graph gives acceleration

Suitable Grade Level

Grades 9-12