# Request for equations

Hi

Does anyone know the projectile motion equations in which the acceleration is NOT constant?

## Answers and Replies

JasonRox
Homework Helper
Gold Member
Learn Calculus.

That's all you need.

ahh.....

Isn't there an equation(s) derived from the kinematic ones i can just apply?

Integral
Staff Emeritus
Science Advisor
Gold Member
There is no way that anybody can guess what you are asking for. You will have to ask an understandable question.

As for variable accelerations, just apply Newtons 3rd:

F=ma

Nothing said:
Hi

Does anyone know the projectile motion equations in which the acceleration is NOT constant?
Isn't there an equation(s) derived from the kinematic ones i can just apply?

I believe you probably already know the standard proceedure here, Nothing.
Usually, beginning with F = ma,
just take the derivative of both sides of the equation since you are looking for the time rate of change of accel.

dF/dt = m(dA/dt)

However, the effectiveness of this equation goes beyond the original assumptions in Newton's law. In cases of rapid change of acceleration a modification of Newton's law is probable. :surprised

Is that what you are getting at?

Creator

F=ma is a differential equation since $a =d^2 x /dt^2$ with x, a and F vectors. Given a certain force you can find the velocity or position as a function of time by integrating the force respectively one or two times. But you indeed need to know some calculus for that...

Alkatran
Science Advisor
Homework Helper
Is the change in acceleration constant?

Doesnt:
Position = Sum(x(i)*t^i/i!)

where i goes from 0 to infinity, x(0) is initial position, x(1) is inital speed, x(2) is inital acceleration, etc....

ok u know that equation:

y = v0 sin (theta) - 0.5at^2 ?

where v0 sin (theta) is the vertical component the muzzle velocity

is there a counterpart where a is not constant?

arildno
Science Advisor
Homework Helper
Gold Member
Dearly Missed
Sure, you have:
$$y(t)=v_{0}t\sin\theta-\int_{0}^{t}(\int_{0}^{\tau}a(s)ds)d\tau$$

thanks arildno, that really helped. 