Molarity Molality Normality and Mass Percent Worksheet II Answer - Free Printable

Problem Analysis and Solution

The problem consists of two main parts:

1. Interpreting a Velocity-Time Graph (Part 1)
2. Graphing Position vs. Time and Calculating Velocity (Part 2)

Let's solve each part step by step.

---

## Part 1: Velocity-Time Graph Analysis

The velocity-time graph provided shows the velocity of a car as a function of time. The graph is plotted with:
- Velocity (km/h) on the vertical axis.
- Time (hours) on the horizontal axis.

Questions and Solutions:

#### a. At what time did the car start?
- The car starts at the point where the time is zero (`t = 0` hours).
- Answer: The car started at 0 hours.

#### b. At what time did the car have the greatest velocity?
- The greatest velocity corresponds to the highest point on the graph.
- From the graph, the maximum velocity occurs around 0.3 hours.
- Answer: The car had the greatest velocity at 0.3 hours.

#### c. What was the greatest velocity?
- The greatest velocity can be read from the y-axis at the peak of the graph.
- The peak value appears to be approximately 80 km/h.
- Answer: The greatest velocity was 80 km/h.

#### d. At what time(s) was the car accelerating?
- Acceleration occurs when the velocity is increasing over time. This corresponds to the sections of the graph where the slope is positive.
- From the graph:
- The car is accelerating from 0 hours to 0.3 hours (the upward-sloping section).
- Answer: The car was accelerating from 0 to 0.3 hours.

#### e. How fast was the car going at 1.0 hour?
- To find the velocity at 1.0 hour, locate the point on the graph where `t = 1.0 hour` and read the corresponding velocity.
- At 1.0 hour, the velocity appears to be approximately 40 km/h.
- Answer: The car was going 40 km/h at 1.0 hour.

#### f. What is the acceleration at 0.9 hour?
- Acceleration is the rate of change of velocity with respect to time, which corresponds to the slope of the velocity-time graph.
- At 0.9 hours, the graph shows a flat line (horizontal segment), indicating that the velocity is constant.
- A flat line means the slope is 0, so the acceleration is 0 m/s².
- Answer: The acceleration at 0.9 hours is 0 m/s².

---

## Part 2: Position-Time Graph and Velocity Calculation

The table provides the positions of two cars (CAR I and CAR II) at different times. We need to:
1. Plot the position vs. time for each car.
2. Calculate the velocity of each car using the graph.

Given Data:

| Time (min) | CAR I (km) | CAR II (km) |
|------------|------------|-------------|
| 0 | 0 | 0 |
| 2 | 2.5 | 1.5 |
| 4 | 5.0 | 3.0 |
| 6 | 7.5 | 4.5 |
| 8 | 10.0 | 6.0 |

Step 1: Plot the Position vs. Time Graph

#### For CAR I:
- At `t = 0 min`, position = 0 km.
- At `t = 2 min`, position = 2.5 km.
- At `t = 4 min`, position = 5.0 km.
- At `t = 6 min`, position = 7.5 km.
- At `t = 8 min`, position = 10.0 km.

#### For CAR II:
- At `t = 0 min`, position = 0 km.
- At `t = 2 min`, position = 1.5 km.
- At `t = 4 min`, position = 3.0 km.
- At `t = 6 min`, position = 4.5 km.
- At `t = 8 min`, position = 6.0 km.

Plot these points on a graph with:
- Time (min) on the x-axis.
- Position (km) on the y-axis.

#### Observations:
- Both graphs will be straight lines because the positions increase linearly with time.

Step 2: Calculate the Velocity of Each Car

Velocity is given by the formula:
\[
\text{Velocity} = \frac{\Delta \text{Position}}{\Delta \text{Time}}
\]

#### For CAR I:
- Choose any two points from the data. Let’s use `(0, 0)` and `(8, 10.0)`:
\[
\text{Velocity of CAR I} = \frac{10.0 \, \text{km} - 0 \, \text{km}}{8 \, \text{min} - 0 \, \text{min}} = \frac{10.0 \, \text{km}}{8 \, \text{min}} = 1.25 \, \text{km/min}
\]

#### For CAR II:
- Choose any two points from the data. Let’s use `(0, 0)` and `(8, 6.0)`:
\[
\text{Velocity of CAR II} = \frac{6.0 \, \text{km} - 0 \, \text{km}}{8 \, \text{min} - 0 \, \text{min}} = \frac{6.0 \, \text{km}}{8 \, \text{min}} = 0.75 \, \text{km/min}
\]

Final Answers for Part 2:

- Velocity of CAR I: 1.25 km/min
- Velocity of CAR II: 0.75 km/min

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## Final Answer Summary

1. Part 1:
- a. The car started at 0 hours.
- b. The car had the greatest velocity at 0.3 hours.
- c. The greatest velocity was 80 km/h.
- d. The car was accelerating from 0 to 0.3 hours.
- e. The car was going 40 km/h at 1.0 hour.
- f. The acceleration at 0.9 hours is 0 m/s².

2. Part 2:
- Velocity of CAR I: 1.25 km/min
- Velocity of CAR II: 0.75 km/min

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
\text{Part 1:} \\
\text{a. 0 hours} \\
\text{b. 0.3 hours} \\
\text{c. 80 km/h} \\
\text{d. 0 to 0.3 hours} \\
\text{e. 40 km/h} \\
\text{f. 0 m/s²} \\
\\
\text{Part 2:} \\
\text{CAR I: 1.25 km/min} \\
\text{CAR II: 0.75 km/min}
\end{array}
}
\]