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)?
a = 6500/60
then divide by 9.8
11.05
To find the average acceleration of the intercontinental ballistic missile, we can use the equation:
average acceleration = (final velocity - initial velocity) / time
The final velocity of the missile is given as 6.50 km/s, but we need to convert it to m/s. Since 1 km/s is equal to 1000 m/s, we have:
final velocity = 6.50 km/s × 1000 m/s/km = 6,500 m/s
The initial velocity is 0 m/s since the missile starts from rest.
Using the given time of 60.0 s, we plug these values into the equation to find the average acceleration:
average acceleration = (6,500 m/s - 0 m/s) / 60.0 s
= 6,500 m/s / 60.0 s
= 108.33 m/s²
So, the average acceleration of the intercontinental ballistic missile is approximately 108.33 m/s².
To find the average acceleration in multiples of g (9.80 m/s²), we divide the average acceleration by the acceleration due to gravity:
average acceleration in multiples of g = average acceleration / g
= 108.33 m/s² / 9.80 m/s²
≈ 11.05 g
Therefore, the average acceleration is approximately 108.33 m/s² and 11.05 times the acceleration due to gravity (g).
To find the average acceleration of the missile, we can use the basic formula:
acceleration = (change in velocity / time)
1. First, let's convert the given speed from km/s to m/s:
6.50 km/s = 6.50 × 1000 m/s = 6500 m/s
2. Next, we are given the time it takes for the missile to accelerate:
time = 60.0 s
3. Now, let's calculate the change in velocity:
change in velocity = final velocity - initial velocity
Since the missile starts from rest, the initial velocity is 0 m/s.
Thus, the change in velocity is equal to the final velocity:
change in velocity = 6500 m/s
4. Finally, we can calculate the average acceleration:
acceleration = change in velocity / time
acceleration = 6500 m/s / 60 s
acceleration ≈ 108.33 m/s^2
So, the average acceleration of the intercontinental ballistic missile is approximately 108.33 m/s^2.
To find the average acceleration in multiples of g, we can divide the average acceleration by the acceleration due to gravity (9.80 m/s^2):
acceleration in multiples of g = average acceleration / acceleration due to gravity (g)
acceleration in multiples of g = 108.33 m/s^2 / 9.80 m/s^2
acceleration in multiples of g ≈ 11.06 g
Therefore, the average acceleration of the missile is approximately 108.33 m/s^2 and 11.06 times the acceleration due to gravity.