To determine which item had the fastest average speed over the five trials, we need to calculate the average time taken for each object and then convert that into speed.
The formula for speed is: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Here, the distance is 100 centimeters for each object.
First, let's find the average time for each object:
Toy: \[ \text{Average} = \frac{3.1 + 2.9 + 3.0 + 2.9 + 3.1}{5} = \frac{15.0}{5} = 3.0 \text{ seconds} \]
Block: \[ \text{Average} = \frac{3.2 + 3.0 + 3.6 + 3.3 + 3.4}{5} = \frac{16.5}{5} = 3.3 \text{ seconds} \]
Ball: \[ \text{Average} = \frac{2.3 + 2.1 + 2.2 + 2.1 + 2.1}{5} = \frac{10.8}{5} = 2.16 \text{ seconds} \]
Pen: \[ \text{Average} = \frac{1.8 + 1.9 + 2.1 + 1.7 + 1.5}{5} = \frac{9.0}{5} = 1.8 \text{ seconds} \]
Now we'll calculate the average speed for each object:
Speed of Toy: \[ \text{Speed} = \frac{100 , \text{cm}}{3.0 , \text{s}} \approx 33.33 , \text{cm/s} \]
Speed of Block: \[ \text{Speed} = \frac{100 , \text{cm}}{3.3 , \text{s}} \approx 30.30 , \text{cm/s} \]
Speed of Ball: \[ \text{Speed} = \frac{100 , \text{cm}}{2.16 , \text{s}} \approx 46.30 , \text{cm/s} \]
Speed of Pen: \[ \text{Speed} = \frac{100 , \text{cm}}{1.8 , \text{s}} \approx 55.56 , \text{cm/s} \]
From these calculations, we find:
- Toy: 33.33 cm/s
- Block: 30.30 cm/s
- Ball: 46.30 cm/s
- Pen: 55.56 cm/s
Therefore, the item with the fastest average speed over the five trials is the Pen.