Engineers are developing new types of guns that might someday be used to launch satellites as if they were bullets. One such gun can give a small object a velocity of 2.5 km/s while moving it through a distance of only 1.9 cm.
To find the acceleration provided by the gun, we can use the equation of motion:
v^2 = u^2 + 2as
where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance traveled.
Given:
u = 0 (initial velocity, since the object starts from rest)
v = 2.5 km/s = 2,500 m/s
s = 1.9 cm = 0.019 m
Using these values, we can rearrange the equation as follows:
a = (v^2 - u^2) / (2s)
Substituting the given values:
a = (2,500^2 - 0^2) / (2 * 0.019)
Solving this equation:
a ≈ 329,947,368.42 m/s^2
Therefore, the acceleration provided by the gun is approximately 329,947,368.42 m/s^2.