# Request for equations

1. Oct 29, 2004

### Nothing

Hi

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

2. Oct 29, 2004

### JasonRox

Learn Calculus.

That's all you need.

3. Oct 29, 2004

### Nothing

ahh.....

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

4. Oct 30, 2004

### Integral

Staff Emeritus
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

5. Oct 30, 2004

### Creator

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

6. Oct 30, 2004

### da_willem

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...

7. Oct 30, 2004

### Alkatran

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....

8. Oct 30, 2004

### Nothing

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?

9. Oct 30, 2004

### arildno

Sure, you have:
$$y(t)=v_{0}t\sin\theta-\int_{0}^{t}(\int_{0}^{\tau}a(s)ds)d\tau$$

10. Oct 30, 2004

### Nothing

thanks arildno, that really helped.