a race track is 500 meters long.car A moves with a constant velocity of 40m/s, approaching the start line.when car A reaches the starting line, car b, who is waiting stationary at the starting line, accelerates at a rate of 10m/s^2. which car will finish first?

Car A: d = r*t, t = d/r = 500/40 = 12.5 s.

Car B: d = 0.5a*t^2, t^2 = d/0.5a = 500/5 = 100, t = 10 s.

To determine which car will finish first, we need to calculate the time it takes for each car to finish the race.

Let's start by calculating the time it takes for car A to finish the race.

We know that car A is moving with a constant velocity of 40 m/s. The formula to calculate time (t) is:

t = distance / velocity

In this case, the distance is the length of the race track, which is 500 meters, and the velocity is 40 m/s.

Plugging in the values, we get:

t = 500 m / 40 m/s
t = 12.5 seconds

So, car A will take 12.5 seconds to finish the race.

Now, let's calculate the time it takes for car B to finish the race.

Car B starts from rest (zero velocity) and accelerates at a rate of 10 m/s^2.

We can use the following formula to calculate the time taken by an object to reach a certain velocity when starting from rest:

v = u + at

Where,
v = final velocity
u = initial velocity (which is zero in this case)
a = acceleration
t = time taken

We want to find the time (t) for car B to reach a velocity of 40 m/s (the same speed as car A) since both cars will have the same final velocity when finishing the race.

Rearranging the equation, we get:

t = (v - u) / a

Plugging in the values, we get:

t = (40 m/s - 0) / 10 m/s^2
t = 4 seconds

So, car B will take 4 seconds to reach a velocity of 40 m/s.

Comparing the times, we can see that car B takes less time (4 seconds) to reach the same speed as car A, while car A takes 12.5 seconds to finish the race. Therefore, car B will finish the race first.