# Is it possible to integrate acceleration?

• B
Alright so I was just messing around with Lagrangian equation, I just learned about it, and I had gotten to this equation of motion:
Mg*sin{α} - 1.5m*x(double dot)=0

I am trying to get velocity, and my first thought was to integrate with dt, but I didn't know how to. And I'm not even sure it's possible, anyways, thanks!

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osilmag
Gold Member
##\int \sin(x) dx = -\cos(x)##

That is the general form for integrating ##\sin(x)##.

osilmag
Gold Member
##\int d^2x = x dx##

Turns out it's possible to do so;
X(dot)=2/3*gt*sin(α)

I had gotten to this equation of motion:
Mg*sin{α} - 1.5m*x(double dot)=0
Surely you’ve seen ##\ddot x = ## constant.
To find ##\dot x## you use ##\ddot x =\frac{d}{dt}\dot x## and separate.

Another common trick worth knowing is from the chain rule:
$$\frac{d^2x}{dt^2} =\frac{d\dot x}{dt} =\frac{dx}{dt} \frac{d\dot x}{dx} =\dot x \frac{d\dot x}{dx}$$
For example, if you have Newton’s law in the form ##m\frac{d^2x}{dt^2}=F(x)## then the chain rule makes it separable, from which we get the (1-D) work energy theorem (for point masses).