Relative Velocity In One Dimension

Relative velocity is the velocity of one body as observed from the frame of another, computed by vector subtraction of the observer's velocity from the observed body's velocity. For motion along a single line in the same direction, this becomes a simple algebraic subtraction. Taking the direction of travel as positive, the faster train has velocity $+25\text{ m/s}$ and the slower train has velocity $+15\text{ m/s}$. The velocity of the faster train relative to the passenger is $v_{fast}-v_{slow}=25-15=+10\text{ m/s}$, meaning it appears to move forward at 10 m/s. The option 40 m/s is wrong because adding the speeds would only apply if the trains moved in opposite directions. The option 10 m/s opposite to motion has the right magnitude but the wrong sign, since the faster train genuinely pulls ahead. The option 15 m/s simply quotes the slower train's ground speed. This is the standard NCERT result for same-direction relative motion. A key insight is that relative velocity describes motion as perceived within a non-inertial-looking but uniformly moving frame, and the ground frame is recovered simply by adding back the observer's own velocity. As a check, the faster train must appear to advance rather than recede, confirming both the positive sign and the reduced relative magnitude of 10 m/s.