Finding the velocity of a car in a different frame of reference

[Redwaves]

Homework Statement

A car is moving on a road with a initial speed $v = v_0$ and then it starts to speed up with $a_0$ what's the speed of this car in the frame of reference on a second car moving at the speed V.

Relevant Equations

$v' = (v_0 + at) - V$

Here's what I did so far.
The velocity of the first car is $v = v_0 +at$

Frame of reference S = the road
Frame of reference S' = the second car

thus, v' is the speed of the first car in the frame of reference S' and v the speed in the frame of reference S.

Here's what make me doubt.
The Galilean transformation
$v' = v - V$
V should be the speed between S and S', in this case what I wrote is wrong.
V should be $(v_0 + at) - V$, right?

And then, $v' = (v_0 + at) - ((v_0 + at) - V)$ does it make sense ?

 

[Doc Al]

Here's what make me doubt.
The Galilean transformation
$v' = v - V$
V should be the speed between S and S', in this case what I wrote is wrong.
V should be $(v_0 + at) - V$, right?

And then, $v' = (v_0 + at) - ((v_0 + at) - V)$ does it make sense ?

You were correct the first time. V is the speed of the second car (and thus frame S') with respect to S.

Realize that your final equation becomes $v' = (v_0 + at) - ((v_0 + at) - V) = V$. Does that make sense?

 

[Redwaves]

I see. I didn't realize that the road is at rest... Of course the speed between S and S' is V.
Thanks!

 

[PeroK]

Homework Statement:: A car is moving on a road with a initial speed $v = v_0$ and then it starts to speed up with $a_0$ what's the speed of this car in the frame of reference on a second car moving at the speed V.

If someone is going to set questions like this, they ought to be more precise, IMO:

A car is moving on relative to a road with an initial speed velocity $v = v_0$ and then it starts to speed up with accelerate at $a_0$. What's the speed velocity of this car in the frame of reference of a second car moving at the speed velocity V relative to the road.