Answer:
The distance between both cars is 990 m
Explanation:
The equations for the position and the velocity of an object moving in a straight line are as follows:
x = x0 + v0 * t + 1/2 * a * t²
v = v0 + a * t
where:
x = position of the car at time "t"
x0 = initial position
v0 = initial speed
t = time
a = acceleration
v = velocity
First let´s find how much time it takes the driver to come to stop (v = 0). We will consider the origin of the reference system as the point at which the driver realizes she must stop. Then x0 = 0
With the equation of velocity, we can obtain the acceleration and replace it in the equation of position, knowing that the position will be 250 m at that time.
v = v0 + a*t
v-v0 / t = a
0 m/s - 71.0 m/s / t =a
-71.0 m/s / t = a
Replacing in the equation for position:
x = v0* t +1/2 * a * t²
250 m = 71.0 m/s * t + 1/2 *(-71.0 m/s / t) * t²
250 m = 71.0 m/s * t - 1/2 * 71.0 m/s * t
250m = 1/2 * 71.0m/s *t
t = 2 * 250 m / 71.0 m/s = 7.04 s
It takes the driver 7.04 s to stop.
Then, we can calculate how much time it took the driver to reach her previous speed. The procedure is the same as before:
v = v0 + a*t
v-v0 / t = a now v0 = 0 and v = 71.0 m/s
(71.0 m/s - 0 m/s) / t = a
71.0 m/s / t =a
Replacing in the position equation:
x = v0* t +1/2 * a * t²
390 m = 0 m/s * t + 1/2 * 71.0 m/s / t * t² (In this case, the initial position is in the pit, then x0 = 0 because it took 390 m from the pit to reach the initial speed).
390m * 2 / 71.0 m/s = t
t = 11.0 s
In total, it took the driver 11.0s + 5.00 s + 7.04 s = 23.0 s to stop and to reach the initial speed again.
In that time, the Mercedes traveled the following distance:
x = v * t = 71.0 m/s * 23.0 s = 1.63 x 10³ m
The Thunderbird traveled in that time 390 m + 250 m = 640 m.
The distance between the two will be then:
distance between both cars = 1.63 x 10³ m - 640 m = 990 m.
