A cyclist A moves with speed 3.0 m s^-1 to the left (with respect to the road). A second cyclist

step 1 This question covers the concept of the relative velocity and we consider the positive x directi

A cyclist A moves with speed 3.0 m s^-1 to the left (with...

A cyclist $\mathrm{A}$ moves with speed $3.0 \mathrm{m} \mathrm{s}^{-1}$ to the left (with respect to the road). $\mathrm{A}$ second cyclist, $\mathrm{B}$, moves on the same straight-line path as $\mathrm{A}$ with a relative velocity of $1.0 \mathrm{m} \mathrm{s}^{-1}$ with respect to $\mathrm{A}$. (a) What is the velocity of $\mathrm{B}$ with respect to the road? (b) A third cyclist has a relative velocity with respect to $\mathrm{A}$ of $-2.0 \mathrm{m} \mathrm{s}^{-1} .$ What is the velocity of $\mathrm{C}$ with respect to the road?

A cyclist $\mathrm{A}$ moves with speed $3.0 \mathrm{m} \mathrm{s}^{-1}$ to the left (with respect to the road). $\mathrm{A}$ second cyclist, $\mathrm{B}$, moves on the same straight-line path as $\mathrm{A}$ with a relative velocity of $1.0 \mathrm{m} \mathrm{s}^{-1}$ with respect to $\mathrm{A}$.
(a) What is the velocity of $\mathrm{B}$ with respect to the road?
(b) A third cyclist has a relative velocity with respect to $\mathrm{A}$ of $-2.0 \mathrm{m} \mathrm{s}^{-1} .$ What is the velocity of $\mathrm{C}$ with respect to the road?

Key Concepts

Sign Conventions

Sign conventions are used to denote the direction of motion in one-dimensional problems, typically by assigning positive and negative values to different directions. Proper use of sign conventions is crucial when adding or subtracting velocities, as it ensures that the direction of motion is accurately represented in calculations.

Relative Velocity

Relative velocity is the velocity of an object as observed from a particular frame of reference. It involves determining how fast one object appears to be moving in relation to another. This concept is essential in understanding motions when multiple objects are in motion, as it helps in analyzing the dynamics of each object with respect to different observers.

Frame of Reference

A frame of reference is a coordinate system or viewpoint from which measurements like position, velocity, and acceleration are made. In problems involving moving observers, choosing an appropriate frame of reference simplifies the analysis and accurately defines how velocities are perceived relative to different observers.

Velocity Addition

Velocity addition is the principle by which velocities measured in different reference frames can be combined to yield the velocity in another frame. This is typically performed by adding the relative velocity of one object with respect to another to the velocity of that second observer relative to a base frame, ensuring careful attention to direction and sign.

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