Hi! I'm supposed to derive an algebraic formula to solve for the acceleration using one of the linear kinematics formulas of an elevator with a person inside that begins to accelerate from rest moving downward. If it travels a know distance, d, in reaching its max downward speed( unknown values). Assume you have access to a timekeeping device.

So I derived acceleration to be a= (v^2)/2d
Then it asks me if I know the total mass of the elevator and the person inside, how would you determine the net force acting on the elevator?
someone please please let me know if I'm doing the first part correct and please help me with the second part! Thank you!!

mass = m

F is our unknown force up (maybe from cable)
a is constant and negative (down)
there is a constant downward force, the weight, mg
it starts at x = 0, and Vi = 0 (initial speed)

F - mg = - m d^2x/dt^2 note F is up, x is down

-m dx/dt = - m v = - m a t
so
v = a t + a constant which is zero because v = 0 at t = 0
so t = v/a
then
x = integral v dt = a t^2/2 + constant which again is zero
so
x = a (v^2/a^2)/2 = (1/2)v^2/a
or as you said
a = v^2/(2d)

F- m g = -m a
F = m g - m a = m (g - v^2/2d)

Hello! It seems like you have correctly derived the formula for acceleration in terms of velocity and distance. Well done!

To determine the net force acting on the elevator, you need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. Mathematically, this can be written as:

F_net = m * a

Here, F_net represents the net force acting on the elevator, m represents the total mass of the elevator and the person inside, and a represents the acceleration.

Using the acceleration formula you derived earlier, you can substitute that value into the equation:

F_net = m * [(v^2) / (2d)]

By plugging in the known values for mass (m) and the derived formula for acceleration, you can calculate the net force (F_net) acting on the elevator.

I hope this helps! Let me know if you have any further questions.