Two cars moving in the same direction have speeds of 100 kmh ^ -1 and 130 kmh ^ -1 . What is the velocity of…

Analyze the question Two cars travel in the same direction. We want the velocity of the faster car relative to the slower car, which is what an observer sitting in the slower car would measure.

Concept: Relative velocity For two objects moving along the same line, the velocity of A relative to B is:

v(A relative to B) = v_A − v_B

When both move in the same direction, you subtract the speeds. (You add them only when they move in opposite directions.)

Solution

• Velocity of the faster car, v_A = 130 km/h
• Velocity of the slower car, v_B = 100 km/h

v(relative) = 130 − 100 = 30 km/h

To the observer in the slower car, the faster car appears to pull ahead at 30 km/h. The observer's own 100 km/h is "cancelled out" because they are moving along with it.

Checking the options

• A. 30 km/h: matches our working.
• B. 130 km/h: this is the speed relative to the ground, not to the slower car.
• C. 200 km/h: not meaningful here, and the unit is wrong.
• D. 230 km/h: this is the sum of the speeds, which applies only to opposite directions.

Exam tip Ask yourself two things:

• Same direction? Subtract the speeds.
• Opposite directions? Add the speeds.

Also, the relative velocity is always measured with respect to the observer, so the observer's own speed is the one you subtract.