Understanding Equations of Motion: Differentiating with Respect to Time

[AStaunton]

I was just thinking about equation of motion:

s=x_0+ut+1/2at^2 where u is initial velocity

diff w.r.t.t to find velocity at a given time :

ds/dt=u+at

My question is, why was it so simple to differentiate w.r.t.t, as "u" is a function of "t" and "a" is a function of t.
But in my differentiation step, these were both treated as constants, why is that?

 

[Gunthi]

Both u and a are independent of time, only v and t vary in your equation.

 

[AStaunton]

ok..I thought that the definition u=dx/dt and a=d^2x/dt^2 implied that they were functions of t...

 

[AStaunton]

although maybe I'm getting myself confused with the units?:

u has units ms^-1 and a has ms^-2...

but the fact that they have time units doesn't necessarily mean they are functions of time.

 

[MOG_Manuel]

The initial velocity is not dependent from time, it's a given value. Same with acceleration in that problem.

Velocity, however, is dependent from time, and it's ds/dt.