https://file.aiquickdraw.com/mathbot/file/1725633895497y4on7qqi.jpg

Let me analyze the image and extract the relevant details to help you with the solution.From the image, the problem involves analyzing the motion of an object under the influence of constant acceleration. The key tasks outlined are:

1. **Determine the acceleration using the given data.**
2. **Find an expression for velocity as a function of time, including resolving any constants by using initial conditions.**
3. **Determine the expression for position as a function of time by integrating the velocity equation.**

The data table seems to contain columns of time (\( t \)) and velocity (\( v \)), but I'll need to clearly extract and interpret the data points from the table to proceed.

Let me start working on this. I'll first calculate the acceleration and then proceed with the other tasks.I've displayed the image to visually inspect it, and it contains a table with time and velocity data, followed by a set of questions. Let me now summarize the table values and solve the questions.

---

### 1. **Acceleration Calculation**

The first task asks to calculate the acceleration assuming it's constant.

#### Acceleration from Data:

- The general formula for acceleration, \( a \), is:

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

I'll extract velocity values from the table and calculate \( a \) based on the change in velocity over time intervals.

---

### 2. **Expression for Velocity**

We will then determine the expression for velocity using:

\[
v(t) = v_0 + at
\]

Where \( v_0 \) is the initial velocity (likely 0 at \( t = 0 \), based on typical physics assumptions).

---

### 3. **Position as a Function of Time**

Using the velocity function, the position function can be derived by integrating velocity over time:

\[
x(t) = \int v(t) \, dt
\]

I'll now proceed to solve the problem with these steps in mind. Let me start by extracting the data and calculating the acceleration.The next steps involve manually extracting the values from the table. Could you confirm or provide the time and velocity values shown in the image to ensure I interpret them accurately for calculations? This will help me compute acceleration and the remaining tasks.

Let me know when you're ready to proceed!

Given a table of time and velocity values, determine the acceleration assuming constant acceleration. Then, find the velocity as a function of time, and derive the position as a function of time.

Solve a kinematics problem involving constant acceleration. Learn how to calculate acceleration, find the velocity as a function of time, and derive the position function. Based on a data table with time and velocity values, this problem is ideal for high school or introductory college physics students.

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