When 2 cars a and b are next to one another, they are traveling in the same dierection with speeds va and vb, respectively. if b maintains its constant speed, while a begins to decelerate at a a, determine the distance d between the cars at the instant a stops.

(Va / a) ((Va/2) - Vb)

Explanation:

The two cars are travelling in the same direction and with speed Va and Vb

Motion of A

since a come to a stop

V = u + at where u = Va and final velocity equals to zero

0 = Va + at

-Va / a = t

t = Va / a since a is deceleration

Distance travel by A

V² = Va² + 2a (Sa) where V = 0 where (Sa) is the distance of A

- Va² = - 2aSa since a is decelerating

Va² / 2 a = Sa

Motion of B

distance converted by B

Sb = Vbt

where t is the motion is observed in the same time

Sb = Vb * Va/a

distance between them

Sa - Sb = (Va² / 2 a) - (Vb * Va/a) = (Va / a) ((Va/2) - Vb)