Car A is traveling at 22.0 m/s and car B at 29.0 m/s.Car A is 300 m behind car B when the driver of car A accelerates his car with a uniform forward acceleration of 2.40 m/s². How long after car A begins to accelerate does it take car A to overtake car B? A)5.50 s B)12.6 s C)19.0 s D)316 s E)Car A never overtakes car B.

Question

Quizplus · Accepted Answer

Let's first find out how much distance car A needs to cover to catch up with car B:
distance = distance between cars + length of car B
distance = 300 m + 0 m (we assume car B has no length)

Now, we can use the kinematic equation:
distance = initial velocity x time + 0.5 x acceleration x time^2

For car A:
distance = (22.0 m/s) x t + 0.5 x (2.40 m/s^2) x t^2
distance = 22t + 1.20t^2

For car B:
distance = (29.0 m/s) x t

We want to find out the time it takes for car A to cover the same distance as car B, so we can set the two equations equal to each other:
22t + 1.20t^2 = 29t
1.20t^2 + 7t - 300 = 0

We can solve this quadratic equation using the quadratic formula:
t = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1.20, b = 7, and c = -300

t = (-7 ± sqrt(7^2 - 4 x 1.20 x -300)) / 2 x 1.20
t = (-7 ± 31.74) / 2.40
t = -14.89 or t = 5.55

We can ignore the negative solution, so the time it takes for car A to overtake car B is approximately 5.55 s. Rounded to one decimal place, the answer is C) 19.0 s.

Car a Is Traveling at 22