Help with a Physics acceleration problem?

Question

Engineers are developing new types of guns that might someday be used to launch satellites as if they were small bullets. One such gun can give a small object a velocity of 3.5 km/s, moving it through only 2.0 cm.

a. What acceleration does the gun give this object?

b. Over what time interval does the acceleration take place?

I'm not exactly sure what the question is asking or saying; step-by-step help would be appreciated.

Also, what does it mean when it says it moves a small object through 2.0 cm?

Answer 1

They mean that in moving the distance 2.0 cm the gun can accelerate a small object up to 3.5 km/s.

This means that the small object is starting at rest so you have

Given: vf= 3.5 km/s, v0= 0 km/s, x0= 0 km, xf=2.0 cm

vf= final velocity, v0 = initial velocity, x0= starting distance, xf= final distance, a = acceleration, t=time, ^(  )=exponent

Find: a and t

First convert everything to kilometers

(2.0 cm)(1 m/ 100 cm)(1 km/ 1000 m)= 2*10^-5 km

vf^2-v0^2=(2)(a)(xf-x0)

(3.5 km/s km/s)^2 - (0.0 km/s)^2 = (2)(a)(2*10^-5 km)

12.25 km^2/s^2 = (2)(2*10^-5 km)(a)

(12.25 km^2/s^2) / (2 *2*10^-5 km) = a

3.1*10^5 km/s^2 = a

b.) vf=v0+at

    3.5 km/s = 0 km/s +3.1*10^5 km/s^2(t)

    (3.5 km/s) / (3.1*10^5 km/s^2) = t

    1.14*10^-5 s = t