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 first need to determine the change in velocity and the time over which the change occurred.
Given:
Initial Velocity (Vo) = 0 m/s (as the missile starts from rest)
Final Velocity (V) = 6.50 km/s = 6,500 m/s
Time (t) = 60.0 s
The change in velocity (∆V) is given by:
∆V = V - Vo
∆V = 6,500 m/s - 0 m/s
∆V = 6,500 m/s
The average acceleration (a) is calculated using the equation:
a = ∆V / t
a = 6,500 m/s / 60.0 s
a = 108.33 m/s² (rounded to two decimal places)
To express the average acceleration in multiples of g, we divide the calculated value by the acceleration due to gravity (g = 9.80 m/s²):
a (in multiples of g) = a / g
a (in multiples of g) = 108.33 m/s² / 9.80 m/s²
a (in multiples of g) = 11.05
Therefore, the average acceleration of the missile is approximately 108.33 m/s² or 11.05 times the acceleration due to gravity (g).