Consider two toy cars. Car A starts from rest and speeds up with constant acceleration for a time delta t until it reached a speed of v and then continues to travel at this speed. At the moment car A reaches its maximum speed, car B, starting at rest from the same point that car A started from, speeds up with constant acceleration.

Determine the ratio Vb/Va where is the speed of car B at the moment it passes car A. Simplify your answer as much as possible. What it the limit Vb/Va as acceleration B approaches 0?

To determine the ratio Vb/Va, we need to analyze the motion of both cars and find their respective speeds at the moment they pass each other.

Let's denote the acceleration of car A as "a" and the acceleration of car B as "b". Since both cars start from rest, their initial velocities are zero.

For car A:
Using the basic equation of motion, we can calculate its speed after time delta t: v = u + at,
where
v = final velocity = speed of car A = Va
u = initial velocity = 0
a = constant acceleration of car A

So, Va = at.

On the other hand, for car B:
Using the same equation of motion, we can calculate its speed when it reaches the point where car A is located: v = u + at,
where
v = speed of car B = Vb
u = initial velocity = 0
a = constant acceleration of car B
t = time taken by car A to reach its maximum speed

But at the moment car B passes car A, car A would have traveled for a time t. Therefore, the time taken by car B to reach this point is also t.

So, Vb = at.

Now, we can determine the ratio Vb/Va:
(Vb/Va) = (at)/(at) = 1.

Therefore, the ratio Vb/Va is always equal to 1, regardless of the values of the acceleration.

Now let's consider the limit Vb/Va as acceleration B approaches 0:
When acceleration B approaches 0, the speed of car B becomes constant, meaning it does not change while it passes car A. In this case, as the acceleration approaches zero, the speed of car B becomes equal to the maximum speed of car A (Va). Therefore, the limit of Vb/Va as acceleration B approaches 0 is equal to 1.