Question

Two cars A and B are 100m apart moving towards each other with

Answer 1

Let car A's starting position be the origin, so that its position at time t is

A: x = (40 m/s) t

and car B has position at time t of

B: x = 100 m - (60 m/s) t

They meet when their positions are equal:

(40 m/s) t = 100 m - (60 m/s) t

(100 m/s) t = 100 m

t = (100 m) / (100 m/s) = 1 s

so the cars meet 1 second after they start moving.

They are 100 m apart when the difference in their positions is equal to 100 m:

(40 m/s) t - (100 m - (60 m/s) t) = 100 m

(subtract car B's position from car A's position because we take car A's direction to be positive)

(100 m/s) t = 200 m

t = (200 m) / (100 m/s) = 2 s

so the cars are 100 m apart after 2 seconds.