To find the position of car A with respect to car B after 15 minutes, we need to consider their relative displacement.

Since both cars are moving along a straight path starting from the same point, we can consider their relative velocity as the difference between their individual velocities.

Given: Speed of car A (v_A) = 40 km/h Speed of car B (v_B) = 60 km/h

We need to find their relative displacement after 15 minutes (which is 15/60 = 1/4 hours).

Step 1: Convert the speeds to meters per second (m/s) for uniform units. Speed of car A (v_A) = 40 km/h = 40 * (1000 m / 3600 s) = 40000/3600 m/s ≈ 11.11 m/s Speed of car B (v_B) = 60 km/h = 60 * (1000 m / 3600 s) = 60000/3600 m/s ≈ 16.67 m/s

Step 2: Find the relative velocity (v_rel) of car A with respect to car B. v_rel = v_A - v_B v_rel ≈ 11.11 m/s - 16.67 m/s ≈ -5.56 m/s

The negative sign indicates that car A is moving in the opposite direction to car B.

Step 3: Calculate the relative displacement (d_rel) after 15 minutes (1/4 hours) using the formula: d_rel = v_rel * time

d_rel ≈ -5.56 m/s * (1/4) hours ≈ -5.56 m/s * 900 seconds ≈ -5004 meters

The negative sign in the displacement indicates that car A is 5004 meters behind car B after 15 minutes.

So, the position of car A with respect to car B after 15 minutes is approximately 5004 meters behind car B.