Can you help me understand and solve this question:
A bullet is fired vertically upwards with an initial velocity of u. Form a second order differential equation for acceleration and by integrating twice find an equation for the displacement s traveled by the bullet in terms of time t from firing.
I cannot wrap my head around this. I haven't done any work, don't know even how to start. All I know is that v(t)=u−gt, where
v(t) is the velocity at time t, u is the initial velocity and −g is the earth acceleration. From this it follows that when t=0 the velocity v(t) will be equal to the initial velocity u; and at a certain point of time, the velocity v(t) will be equal to zero. Do I need to differentiate the v(t)=u−gt equation to get to the equation for the acceleration? And then integrate the acceleration equation twice? I am not even sure that v(t)=u−gt is the right velocity equation.