SOLUTION: Two cars, A and B, are travelling in the same direction, although car A is 182 m behind car B. The speed of A is 24.3 m/s, and the speed of B is 18.4 m/s. (a) How much time does

Question 1191827: Two cars, A and B, are travelling in the same direction, although car A is 182 m behind car B. The speed of A is 24.3 m/s, and the speed of B is 18.4 m/s.
(a) How much time does it take for A to catch B?
(b) If at the end of this time, A begins to decelerate at 2.5 m/s2, calculate the total distance travelled by A.
Answer by ikleyn(52756) (Show Source): You can put this solution on YOUR website!
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Two cars, A and B, are travelling in the same direction, although car A is 182 m behind car B.
The speed of A is 24.3 m/s, and the speed of B is 18.4 m/s.
(a) How much time does it take for A to catch B?
(b) If at the end of this time, A begins to decelerate at 2.5 m/s2, calculate the total distance travelled by A.
~~~~~~~~~~~~~~~~~

(a)  time for A to catch B =  = 30.85 seconds (rounded).    ANSWER


     We divide the separating distance by the approaching (= relative) speed.



(b)  Solve it in three steps.


     Step 1.  The time decelerating to get full stop =  = 9.72 seconds.   


     Step 2.  The decelerating distance =  =  = 118.1 meters (rounded).    



     Step 3.  The total distance is the sum  24.3*30.85 + 118.1 = 867.76 m.    ANSWER

Solved.

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