Question

how to derivate v =dx /dt

Answer 1

so here is the explaination hope u will like it

Let us assume, for the time being:

v=v(x,t)

i.e Suppose velocity is function of space and time for a particle, (1D Motion)

By chain rule:

a= dv/dt=∂v/∂x dx/dt+ ∂v/∂t dt/dt

a=∂v/∂x dx/dt+ ∂v/∂t

Now is the time to discuss about ∂v/∂t : Since the particle can be at one and only one location at given time, say ‘t’, its velocity at any point cannot vary with time, since the point itself is not varying. Note that ∂v/∂t represent the change in velocity at a constant x. Which is not possible in this case of a particle (I presume this, as you have not specified the system). So the term ∂v/∂t=0.

Thus we have

a=∂v/∂x dx/dt

Or

a=dv/dx dx/dt=v dv/dx

Another Way:

v=v(x)

x=x(t)

You must realize why we have written v as a function of x only, not t.

X as a function of t is easy to understand.

dv/dx= dv/dx× dx/dt

a=v dv/dx

Answer 2

dw = f.dt

f = q.v

dw = q.v.dt

o = 180'

dw = q.vdtcos180'

dw = qvdt(1)

dw = qvdr

dw/q. = vdr

v = dv/dt H.P