Question

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) (a) 1.08×10⁻² m/s², (b) 1.10×10⁻³ g
b) (a) 1.10×10⁻² m/s², (b) 1.12×10⁻³ g
c) (a) 1.08×10⁻² m/s², (b) 1.12×10⁻³ g
d) (a) 1.10×10⁻² m/s², (b) 1.10×10⁻³ g

Answer 1

The average acceleration of an intercontinental ballistic missile reaching 6.50 km/s in 60 seconds is 108.33 m/s² or approximately 11.06 times the acceleration due to gravity (g).

Step-by-step explanation:

To calculate the average acceleration of an intercontinental ballistic missile going from rest to a suborbital speed of 6.50 km/s in 60.0 s, we'll first need to convert the final velocity to meters per second. The conversion from kilometers per second to meters per second is done by multiplying the speed by 1000, so the final velocity is 6.50 km/s × 1000 = 6500 m/s.

Now, using the formula for acceleration, a = (Δv / Δt), where Δv is the change in velocity and Δt is the change in time, we plug in our values:
a = (6500 m/s) / (60.0 s) = 108.33 m/s².

To find acceleration in multiples of g, we divide the acceleration by the acceleration due to gravity (9.80 m/s²):
a in g's = 108.33 m/s² / 9.80 m/s² ≈ 11.06 g. Therefore, the correct answer is the acceleration in m/s² is 108.33 and in multiples of g is 11.06.