Deriving Motion Equation from Newton's Second Law

[erok81]

Homework Statement

An object is dropped from a height above a pool of water.

Start with Newton’s 2nd law, F = ma and use the general expression for acceleration, a_y=d²y/dt² to generate a differential equation

Homework Equations

F=ma

-mg=m d²y/dt²

The Attempt at a Solution

We had this problem in our problem solving session last week. My physics I class I never learned how to derive anything, so I am always on a quest to figure these out. This is one I cannot do. I can set up as far as I have. I see I can cancel the m's and then integrate both sides, but I cannot get to the correct answer.

The answer is a regular equation of motion - y₁=y₂+vt - 1/2gt².

How does one approach this problem?

 

[LCKurtz]

Homework Statement

An object is dropped from a height above a pool of water.

Start with Newton’s 2nd law, F = ma and use the general expression for acceleration, a_y=d²y/dt² to generate a differential equation

Homework Equations

F=ma

-mg=m d²y/dt²

The Attempt at a Solution

We had this problem in our problem solving session last week. My physics I class I never learned how to derive anything, so I am always on a quest to figure these out. This is one I cannot do. I can set up as far as I have. I see I can cancel the m's and then integrate both sides, but I cannot get to the correct answer.

The answer is a regular equation of motion - y₁=y₂+vt - 1/2gt².

How does one approach this problem?

You have the right equation to start.

y''(t) = -g

Here's the next step. Integrate once:

y'(t) = -gt + C

Use the velocity at t = 0 to figure out C, then integrate again, getting another constant you will need to figure out from the initial conditions.