Firing men in a capsule from a 220 meter long cannon with final speed of 10.97 km/s. What is the acceleration?

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Answer 1 · 2016-08-06T10:52:26

#a approx 273.5 km "/ sec"^2#

with acceleration a, velocity v and displacement x, if you start with the idea that

#a = (dv) /dt# (and we are treating a as a constant as you want average value)

then
#a color(red)(v) = color(red)(v) (dv) /dt#

#int av \ dt =int v (dv) /dt \ dt#

#a int dx/dt \ dt =int d/dt( v^2/2 ) \ dt#

#ax = v^2/2 + C#

if starting from rest, #x_o = v_o = 0 implies C = 0#

So
#ax = v^2/2 implies a = v^2/(2x)#

and here #a = (10.97^2)/(2*0.22) approx 273.5 km "/ sec"^2#