A car, P, with a velocity of 30 m/s is traveling in the same direction as a car, Q, with a velocity of 20 m/s. The velocity of P relative to Q is

Analyze the question Two cars move in the same direction. We want the velocity of P as seen by someone in car Q (relative velocity).

Concept The velocity of A relative to B is:

v(A relative to B) = v_A − v_B

Both velocities are measured in the same direction. If the cars move the same way, you subtract. If they move in opposite directions, you add the magnitudes.

Solution

• v_P = 30 m/s
• v_Q = 20 m/s

v(P relative to Q) = v_P − v_Q = 30 − 20 = 10 m/s

This means that from Q's point of view, P pulls ahead at 10 m/s.

Checking the options

• A (50 m/s) is what you get by adding, which is only correct if the cars moved in opposite directions.
• B (45 m/s) and C (20 m/s) do not come from any valid operation on these numbers.

Answer: D, 10 m/s

Exam tip: For "relative to" questions, first check the directions. Same direction means subtract. Opposite directions means add. Remember "A relative to B = A minus B."