The speed of an object can be measured at any time during its motion by using this relation: Speed= Distance covered by the object/ Time taken to cover this distance
As you have said,the physical laws will be the same for moving(with a constant velocity) and stationary objects.So speed is a relative quantity.There is nothing known as absolute speed.
(Example:Right now,is your table in motion?No.So according to you the speed of your table is 'zero'.But if a person passes by you in a motorcycle at a speed of 20(constant velocity),according to him your table won't be at rest,it will be moving at a velocity of 20 along with you.But his seat will be at rest according to him.And what if another person passes by at a speed of 50...?So,What is the actual speed of your table?Is it 0,20 or 50?Who is correct? Actually everyone is correct!Your table does not have any prefence speed.The speed of your table just depends on the frame of refence with which the person measures it.The speed can be measured anything between'0' and 'c'(speed of light),including '0' but not 'c').
2.Suppose I'm on Earth and you are in a spaceship.When I observe your spaceship(according to me),say it is moving with a constant velocity ' a '.Now suppose there is a rocket moving with the same velocity(speed and direction) as your spaceship.Therefore according to me the velocity of the rocket will also be ' a '.But according to you the velocity of the rocket will be '0'.
Now suppose the rocket accelerates suddenly.
You observe that the speed of the rocket has changed from '0' to say 'b' in time say 't'.
But I will observe that the speed of the rocket has changed from 'a' to 'a+b' in time 't'[TIME WILL BE SAME FOR BOTH OF US*].
According to you acceleration of the rocket will be:(b-0)/t=b/t.
According to me acceleration of the rocket will be ((b+a)-a)/t=(b+a-a)/t=b/t.
We did not agree on the speed of the rocket to be same(for me it was 'a' and for you it was '0').But we agree that it's acceleration is same( in our case 'b/t').
And this acceleration 'b/t' will be the same whoever measures it (irrespsctive of his inertial frame).
I hope your doubts are clear......................................
Thanks.
If you still have doubt,your doubt can still be a valid one!
Because,above I've written in caps that ' TIME WILL BE SAME FOR BOTH OF US* '.
But in reality when we are moving at different speeds time won't be the same!!
It will differ by a factor of ' sqrt(1-(v/c)^2) '(where 'v' is the relative velocity)
So our measurement of acceleration 'b/t' of the rocket will vary.
In this case,what you are actually demanding is the explanation of
Albert Einstein's 'Special Theory of Relativity'.