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/ $\mathrm { s }^2$ 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

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

Car a Is Traveling at 22 s2\mathrm { s }^2s2 How Long After Car a Begins to Accelerate Does It

Car a Is Traveling at 22 $\mathrm { s }^2$ How Long After Car a Begins to Accelerate Does It