i want to know three equations of motion

Question

imtiaz7 · Answer

1) vf=vi+at
2) S=vit+1/2 *at^2
3) 2aS=vf^2-vi^2

shamim · Answer

i have doubt abt ur reply @imtiaz

shamim · Answer

explain plz @imtiaz

mrnood · Answer

@shamim 

I think imtiaz is correct.

These refer to motion under CONSTANT acceleration (beware)

vi = initial speed at t0
vf = final speed at t1
a = acceleration 
t = elapsed time   (normally t0 = 0 to t1 = t)
s = distance travelled(displacement) at t1

shamim · Answer

ok

shamim · Answer

understood

shamim · Answer

thanks to help me@ MrNood

mrnood · Answer

IF you have covered any integration calculus you can derive all these from:

acceleration a=dv/dt=constant

Integrate once for velocity  (=ds/dt)

Integrate again for displacement (s) 

(don't forget the constants of integration)

shamim · Answer

hmmmm

mrnood · Answer

$$a = dv/dt$$
$$dv = a dt$$
$$\int\limits_{}^{}dv = \int\limits_{}^{} a dt$$
$$v = at +c$$
but when t = 0 v = vi
Therefore v = vi + at

But  v = ds/dt

So ds/dt = vi + at  (at this point vi is a constant)

so 
$$s=\int\limits_{}^{}(vi + at) dt$$
$$s=v _{i} t + \frac{ 1 }{ 2 }a t^{2}+c$$

now - it is usual ( but not necessary) that s = 0 when t = 0 so in this case c=0
but in general
$$s = s _{0}+v _{i}t+\frac{ 1 }{ 2 }at ^{2}$$