Tectonic plates are large segments of the Earth's crust that move slowly. Suppose one such plate has an average speed of 7.60 cm per year.

(a)

What distance (in m) does it move in 75.0 seconds at this speed?

To solve this problem, we need to calculate the distance moved by the tectonic plate in 75.0 seconds, given its speed of 7.60 cm per year.

### Step-by-Step Calculation:

1. **Convert speed from cm/year to cm/second:**
   \[
   \text{Speed} = 7.60 \, \text{cm/year}
   \]
   We need to convert years to seconds. There are 365.25 days in a year (accounting for leap years), and each day has 24 hours, 60 minutes per hour, and 60 seconds per minute.
   \[
   1 \, \text{year} = 365.25 \times 24 \times 60 \times 60 = 31,557,600 \, \text{seconds}
   \]
   Now, convert the speed:
   \[
   \text{Speed} = \frac{7.60 \, \text{cm}}{31,557,600 \, \text{s}} \approx 2.41 \times 10^{-7} \, \text{cm/s}
   \]

2. **Calculate the distance moved in 75.0 seconds:**
   The distance can be found using the formula:
   \[
   \text{Distance} = \text{Speed} \times \text{Time}
   \]
   Substituting the values:
   \[
   \text{Distance} = (2.41 \times 10^{-7} \, \text{cm/s}) \times 75.0 \, \text{s} = 1.8075 \times 10^{-5} \, \text{cm}
   \]

3. **Convert the distance from cm to meters:**
   Since \(1 \, \text{cm} = 0.01 \, \text{m}\), we convert the result to meters:
   \[
   \text{Distance} = 1.8075 \times 10^{-5} \, \text{cm} \times 0.01 = 1.8075 \times 10^{-7} \, \text{m}
   \]

Thus, the plate moves a distance of approximately \(1.81 \times 10^{-7} \, \text{m}\) in 75.0 seconds.

---

Would you like any further details on the calculation? Here are some related questions for further understanding:

1. How would the distance change if the speed of the plate increased by 10%?
2. What is the distance covered in a full year at this speed in kilometers?
3. How many meters does the plate move in a day?
4. What would the distance be if the time interval were doubled to 150 seconds?
5. How does this calculation relate to the concept of tectonic plate theory?

**Tip:** When dealing with very small distances and long time periods, be mindful of unit conversions to ensure accuracy.

Tectonic plates are large segments of the Earth's crust that move slowly. Suppose one such plate has an average speed of 7.60 cm per year.

(a)

What distance (in m) does it move in 75.0 seconds at this speed?

Discover how to calculate the distance moved by a tectonic plate in 75 seconds at a speed of 7.60 cm/year. This step-by-step solution explains how to convert the speed into cm/second and find the distance in meters. Suitable for students in Grades 8-10.

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