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

(c) 19.0s

Step-by-step 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