The acceleration vector of a particle with position r(t) = (x(t), y(t)) is which of the following?

The acceleration vector of a particle with position r(t) = (x(t), y(t)) is which of the following?

• A. (x''(t), y''(t))
• B. (dx/dt, dy/dt)
• C. (d^3x/dt^3, d^3y/dt^3)
• D. (x(t), y(t))

Answer: (A)

Acceleration is the rate of change of velocity, so for a particle with position r(t) = (x(t), y(t)), its velocity is v(t) = r'(t) = (x'(t), y'(t)). The acceleration is the derivative of velocity, a(t) = v'(t) = r''(t) = (x''(t), y''(t)). Thus the acceleration vector has components given by the second-time derivatives of the coordinates. The first derivatives (x'(t), y'(t)) are velocity, the original position (x(t), y(t)) is position, and the third derivatives (x'''(t), y'''(t)) relate to jerk.

Acceleration is the rate of change of velocity, so for a particle with position r(t) = (x(t), y(t)), its velocity is v(t) = r'(t) = (x'(t), y'(t)). The acceleration is the derivative of velocity, a(t) = v'(t) = r''(t) = (x''(t), y''(t)). Thus the acceleration vector has components given by the second-time derivatives of the coordinates. The first derivatives (x'(t), y'(t)) are velocity, the original position (x(t), y(t)) is position, and the third derivatives (x'''(t), y'''(t)) relate to jerk.