The velocity vector for a particle with position r(t) = (x(t), y(t)) is what?

The velocity vector for a particle with position r(t) = (x(t), y(t)) is what?

• A. (dx/dt, dy/dt)
• B. (d^2x/dt^2, d^2y/dt^2)
• C. (x(t), y(t))
• D. (dy/dt, dx/dt)

Answer: (A)

The velocity vector is the rate of change of position with respect to time. For a particle with position r(t) = (x(t), y(t)), its velocity is the derivative dr/dt. Taking the derivative componentwise gives v(t) = (dx/dt, dy/dt). This vector lies along the direction of motion, and its length is the speed, sqrt[(dx/dt)^2 + (dy/dt)^2]. The position vector itself is r(t). The second derivatives (d^2x/dt^2, d^2y/dt^2) relate to acceleration, not velocity, and swapping components to (dy/dt, dx/dt) isn’t the standard velocity in this setup.

The velocity vector is the rate of change of position with respect to time. For a particle with position r(t) = (x(t), y(t)), its velocity is the derivative dr/dt. Taking the derivative componentwise gives v(t) = (dx/dt, dy/dt). This vector lies along the direction of motion, and its length is the speed, sqrt[(dx/dt)^2 + (dy/dt)^2]. The position vector itself is r(t). The second derivatives (d^2x/dt^2, d^2y/dt^2) relate to acceleration, not velocity, and swapping components to (dy/dt, dx/dt) isn’t the standard velocity in this setup.