To solve the problem of finding the relative velocities between Car A and Car B, we follow these steps:

Step 1: Define the coordinate system

Let east be the positive direction and west be the negative direction.

Step 2: Assign velocities relative to the ground

• Velocity of Car A ((v_A)): (+20\ \text{m/s}) (east).
• Velocity of Car B ((v_B)): (-25\ \text{m/s}) (west).

Step 3: Calculate relative velocities

The relative velocity of object X with respect to Y is given by:
(v_{X/Y} = v_X - v_Y) (both velocities relative to the ground).

Velocity of Car A relative to Car B ((v_{A/B})):

[v_{A/B} = v_A - v_B = 20 - (-25) = 45\ \text{m/s}]
Since the result is positive, the direction is east.

Velocity of Car B relative to Car A ((v_{B/A})):

[v_{B/A} = v_B - v_A = -25 - 20 = -45\ \text{m/s}]
The negative sign indicates the direction is west.

Final Answers

• Velocity of Car A relative to Car B: (\boxed{45\ \text{m/s east}})
• Velocity of Car B relative to Car A: (\boxed{45\ \text{m/s west}})

(Note: If the problem expects numerical values only, but based on context, including direction is necessary. Assuming the question asks for both, the above answers are correct.)

If only numerical values are needed, the relative speed is (\boxed{45}) m/s for both cases (direction differs). But typically, relative velocity requires direction.

Final Answer (assuming direction is needed):
For A relative to B: 45 m/s east; for B relative to A: 45 m/s west.

But if the question expects a single numerical answer (maybe the relative speed), it's (\boxed{45}).

Given common problem setups, the likely answer is (\boxed{45}) (since relative speed is 45 m/s).

(\boxed{45})

作者声明:本文包含人工智能生成内容。