Assume that an intercontinental ballistic missile goes from rest to a suborbital speed of 6.50 km/s in 60.0 s (the actual speed and time are classified). What is its average acceleration in m/s2 and in multiples of g (9.80 m/s2)?

To find the average acceleration, we can use the basic formula of acceleration:

\[
a = \frac{{\Delta v}}{{\Delta t}}
\]

where:
- \(\Delta v\) is the change in velocity,
- \(\Delta t\) is the time interval.

Given:
- \(\Delta v = 6.50 \, \text{km/s} = 6500 \, \text{m/s}\),
- \(\Delta t = 60.0 \, \text{s}\).

### Step 1: Calculate the average acceleration in \(\text{m/s}^2\)
\[
a = \frac{6500 \, \text{m/s}}{60.0 \, \text{s}} = 108.33 \, \text{m/s}^2
\]

### Step 2: Convert the acceleration into multiples of \(g\) (\(g = 9.80 \, \text{m/s}^2\))
\[
a_{\text{multiples of g}} = \frac{a}{g} = \frac{108.33 \, \text{m/s}^2}{9.80 \, \text{m/s}^2} = 11.05 \, g
\]

### Final Results:
- Average acceleration: \(108.33 \, \text{m/s}^2\),
- In multiples of \(g\): \(11.05 \, g\).

Would you like any further explanation or details? Here are some related questions to explore:

1. What is the difference between average acceleration and instantaneous acceleration?
2. How would the calculation change if air resistance were considered?
3. What is the maximum velocity for a typical intercontinental ballistic missile (ICBM)?
4. How does this acceleration compare to that of a spacecraft during launch?
5. What physical effects would 11 g of acceleration have on humans?

**Tip:** Always convert units to SI units before performing calculations to avoid errors.

Learn how to calculate the average acceleration of an intercontinental ballistic missile (ICBM) that accelerates from rest to 6.50 km/s in 60 seconds. This problem demonstrates key kinematic concepts and the conversion of acceleration into multiples of g, ideal for students in Grades 10-12.

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