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 an acceleration of 2.40 m/s². How long 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.

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Quizplus · Accepted Answer

To find the time it takes for car A to overtake car B, we set up the equations for their positions as functions of time and solve for when they are equal. Car A's position is given by the equation: $ x_A = 22t + 0.5 \times 2.4 \times t^2 $. Car B's position is given by: $ x_B = 29t + 300 $. Setting $ x_A = x_B $ and solving for $ t $, we get a quadratic equation: $ 1.2t^2 - 7t - 300 = 0 $. Solving this equation gives $ t \approx 19.0 $ seconds.

Car a Is Traveling at 22