Question

Marina conducts an experiment investigating Newton’s first law of motion by sliding several objects across a smooth floor. The time in seconds it took for each object to travel 100 centimeters is recorded in the following table.

Newton’s First Law of Motion
Surface: Smooth Floor – Time in Seconds
Object Trial 1 Trial 2 Trial 3 Trial 4 Trial 5
Toy 3.1 2.9 3.0 2.9 3.1
Block 3.2 3.0 3.6 3.3 3.4
Ball 2.3 2.1 2.2 2.1 2.1
Pen 1.8 1.9 2.1 1.7 1.5
Which of the items had the fastest average speed over the five trials?

Answer 1

To determine which item had the fastest average speed over the five trials, we first need to calculate the average time taken for each object based on the trials recorded. Then, we can use the speed formula:

\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}}
\]

Since the distance for all trials is 100 centimeters, we can calculate the average speed by using the average time for each object.

1. **Calculating the Average Time for Each Object:**

- **Toy:**
\[
\text{Average time} = \frac{3.1 + 2.9 + 3.0 + 2.9 + 3.1}{5} = \frac{15.0}{5} = 3.0 \text{ seconds}
\]

- **Block:**
\[
\text{Average time} = \frac{3.2 + 3.0 + 3.6 + 3.3 + 3.4}{5} = \frac{16.5}{5} = 3.3 \text{ seconds}
\]

- **Ball:**
\[
\text{Average time} = \frac{2.3 + 2.1 + 2.2 + 2.1 + 2.1}{5} = \frac{10.8}{5} = 2.16 \text{ seconds}
\]

- **Pen:**
\[
\text{Average time} = \frac{1.8 + 1.9 + 2.1 + 1.7 + 1.5}{5} = \frac{9.0}{5} = 1.8 \text{ seconds}
\]

2. **Calculating the Average Speed for Each Object:**

- **Toy Speed:**
\[
\text{Speed} = \frac{100 \text{ cm}}{3.0 \text{ s}} = 33.33 \text{ cm/s}
\]

- **Block Speed:**
\[
\text{Speed} = \frac{100 \text{ cm}}{3.3 \text{ s}} = 30.30 \text{ cm/s}
\]

- **Ball Speed:**
\[
\text{Speed} = \frac{100 \text{ cm}}{2.16 \text{ s}} = 46.30 \text{ cm/s}
\]

- **Pen Speed:**
\[
\text{Speed} = \frac{100 \text{ cm}}{1.8 \text{ s}} = 55.56 \text{ cm/s}
\]

3. **Conclusion:**
The pen had the fastest average speed over the five trials, at approximately **55.56 cm/s**.