/sci/ - Science & Math

[Anonymous No.3316306]

<span class="math">
\ddot{x}(t) = {{F_0} \over {m}}
[/spoiler]

<span class="math">
\dot{x}(t) = {{v_0} + {{{F_0} \over {m}}t}}
[/spoiler]

I can't remember the method of integration that he used. Can /sci/ help me out?

It's the integration of Newton's second law btw.

[Anonymous No.3316322]

To be clear. I can user stand it just from the definition of integration but I can't recall the mathematical method I would use if I didn't know prior hand the relationship between displacement, velocity, acceleration, time...etc

[Anonymous No.3316336]

<div class="math">\ddot{x}=\frac{\mathrm{d} \dot{x}}{\mathrm{d} t}</div>

Its the definition of acceleration in 1 dimension, then he passed dt to the other side and integrated.

[Anonymous No.3316349]

>>3316336

Yes. I can understand that. I just don't know how he managed to integrate:

<span class="math">
{{F_0} \over {m}} dt
[/maht][/spoiler]

[Anonymous No.3316355]

<div class="math">\ddot{x}(t) = {{F_0} \over {m}}</div>
<div class="math">\int \frac{\mathrm{d} \dot{x}(t)}{\mathrm{d} t} dt= \int{{F_0} \over {m}} dt</div>
<div class="math">\dot{x}(t) = {{v_0} + {{{F_0} \over {m}}t}}</div>

[Anonymous No.3316358]

>>3316349

Since F/m is contant

<div class="math">\int_{0}^{t}\frac{F}{m}dt=\frac{F}{m}\int_{0}^{t}dt=\frac{F}{m}t+C</div>

Now we set t=0 for C which must equal the initial speed

[Anonymous No.3316373]

>>3316358

>Since F/m is contant

Ofcource! Thanks and have a good day!