Question

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) 12.6 s B) 5.50 s C) 19.0 s D) 316 s E) Car A never overtakes car B.

Answer 1

Answer:

(c) 19.0s

Explanation:

Given Data

Car A speed v=22.0 m/s

Car B speed v=29.0 m/s

Car A distance S=300 m behind Car B

Car A acceleration a=2.40 m/s²

To find

Time required For Car A to take over Car B

Solution

We can represent Car A Coordinate by using equation of simple motion

$X_{A} =vt+1/2at^{2}\\X_{A} =22t+(1/2)(2.40)t^{2}$

And Coordinates of car B equals

$X_{B}=300+29t$

Car A is overtake car B when:

$X_{A}=X_{B}\\ 22t+(1/2)(2.4)t^{2}=300+29t\\1.2t^{2}-7t-300=0\\ time=19.0s$

Option (C) 19.0s is correct one