SOLUTION: 2 5 worksheet velocity time graphs 1 - Studypool - Free Printable

Problem Analysis:

The task requires us to:
1. Draw velocity vs. time graphs for objects whose motion is described by the given position vs. time graphs.
2. Provide a written description of the motion for each case.

#### Key Concepts:
- The slope of a position vs. time graph gives the velocity at any point in time.
- A constant slope on a position vs. time graph indicates constant velocity.
- A changing slope on a position vs. time graph indicates acceleration or deceleration.

Solution:

#### Problem 5:
##### Position vs. Time Graph:
- The graph is a straight line passing through the origin.
- The slope of the line is constant and positive.

##### Velocity vs. Time Graph:
- Since the slope of the position vs. time graph is constant, the velocity is constant.
- The velocity can be calculated as:
\[
\text{Slope} = \frac{\Delta \text{Position}}{\Delta \text{Time}} = \frac{4 \, \text{m}}{4 \, \text{s}} = 1 \, \text{m/s}
\]
- Therefore, the velocity vs. time graph will be a horizontal line at \( v = 1 \, \text{m/s} \).

##### Written Description:
- The object is moving with a constant velocity of \( 1 \, \text{m/s} \) in the positive direction.

##### Final Answer for Problem 5:
- Velocity vs. Time Graph: A horizontal line at \( v = 1 \, \text{m/s} \).
- Written Description: Constant velocity motion at \( 1 \, \text{m/s} \).

---

#### Problem 6:
##### Position vs. Time Graph:
- The graph shows two distinct segments:
1. From \( t = 0 \) to \( t = 2 \, \text{s} \): The slope is steep and positive.
2. From \( t = 2 \, \text{s} \) to \( t = 5 \, \text{s} \): The slope is less steep and positive.

##### Velocity vs. Time Graph:
- From \( t = 0 \) to \( t = 2 \, \text{s} \):
- The slope of the position vs. time graph is:
\[
\text{Slope} = \frac{\Delta \text{Position}}{\Delta \text{Time}} = \frac{2 \, \text{m}}{2 \, \text{s}} = 1 \, \text{m/s}
\]
- Therefore, the velocity is \( 1 \, \text{m/s} \) during this interval.
- From \( t = 2 \, \text{s} \) to \( t = 5 \, \text{s} \):
- The slope of the position vs. time graph is:
\[
\text{Slope} = \frac{\Delta \text{Position}}{\Delta \text{Time}} = \frac{4 \, \text{m} - 2 \, \text{m}}{5 \, \text{s} - 2 \, \text{s}} = \frac{2 \, \text{m}}{3 \, \text{s}} \approx 0.67 \, \text{m/s}
\]
- Therefore, the velocity is approximately \( 0.67 \, \text{m/s} \) during this interval.

##### Written Description:
- From \( t = 0 \) to \( t = 2 \, \text{s} \), the object moves with a constant velocity of \( 1 \, \text{m/s} \).
- From \( t = 2 \, \text{s} \) to \( t = 5 \, \text{s} \), the object moves with a constant velocity of approximately \( 0.67 \, \text{m/s} \).

##### Final Answer for Problem 6:
- Velocity vs. Time Graph: A horizontal line at \( v = 1 \, \text{m/s} \) from \( t = 0 \) to \( t = 2 \, \text{s} \), followed by a horizontal line at \( v \approx 0.67 \, \text{m/s} \) from \( t = 2 \, \text{s} \) to \( t = 5 \, \text{s} \).
- Written Description: Two intervals of constant velocity: \( 1 \, \text{m/s} \) from \( t = 0 \) to \( t = 2 \, \text{s} \), and \( 0.67 \, \text{m/s} \) from \( t = 2 \, \text{s} \) to \( t = 5 \, \text{s} \).

---

Final Answers:

\[
\boxed{
\begin{array}{l}
\text{Problem 5:} \\
\text{Velocity vs. Time Graph: Horizontal line at } v = 1 \, \text{m/s}. \\
\text{Written Description: Constant velocity motion at } 1 \, \text{m/s}. \\
\\
\text{Problem 6:} \\
\text{Velocity vs. Time Graph: Horizontal line at } v = 1 \, \text{m/s} \text{ from } t = 0 \text{ to } t = 2 \, \text{s}, \text{ then horizontal line at } v \approx 0.67 \, \text{m/s} \text{ from } t = 2 \, \text{s} \text{ to } t = 5 \, \text{s}. \\
\text{Written Description: Two intervals of constant velocity: } 1 \, \text{m/s} \text{ from } t = 0 \text{ to } t = 2 \, \text{s}, \text{ and } 0.67 \, \text{m/s} \text{ from } t = 2 \, \text{s} \text{ to } t = 5 \, \text{s}.
\end{array}
}
\]