In the position vector r(t) = (x(t), y(t)), which statement about x(t) and y(t) is correct?

In the position vector r(t) = (x(t), y(t)), which statement about x(t) and y(t) is correct?

• A. x(t) denotes horizontal position, y(t) denotes vertical position
• B. x(t) denotes horizontal velocity, y(t) denotes vertical velocity
• C. x(t) denotes vertical position, y(t) denotes horizontal position
• D. x(t) denotes speed, y(t) denotes acceleration

Answer: (B)

r(t) = (x(t), y(t)) describes the particle’s location in the plane. The components x(t) and y(t) are the horizontal and vertical positions at time t, respectively. If you want velocity, you differentiate: the horizontal velocity is x'(t) and the vertical velocity is y'(t). The speed is the magnitude of the velocity vector, given by sqrt((x'(t))^2 + (y'(t))^2). Acceleration comes from the second derivatives x''(t) and y''(t). So x(t) is horizontal position, not velocity; velocity is represented by x'(t) and y'(t).

r(t) = (x(t), y(t)) describes the particle’s location in the plane. The components x(t) and y(t) are the horizontal and vertical positions at time t, respectively. If you want velocity, you differentiate: the horizontal velocity is x'(t) and the vertical velocity is y'(t). The speed is the magnitude of the velocity vector, given by sqrt((x'(t))^2 + (y'(t))^2). Acceleration comes from the second derivatives x''(t) and y''(t). So x(t) is horizontal position, not velocity; velocity is represented by x'(t) and y'(t).