Kinematics 2 Duke University（运动学2 杜克大学）.pdf

Physics 53 Kinematics 2 Our nature consists in movement; absolute rest is death. —Pascal Velocity and Acceleration in 3-D We have defined the velocity and acceleration of a particle as the first and second time derivatives of the position, in the special case of one dimensional motion. What is the generalization to motion in two or three dimensions? Simply that the position must now be described by a vector r(t) and the velocity an acceleration are derivatives with respect to time of this vector: dr Velocity: v = dt Velocity and AccelerationVelocity and Acceleration 2 dv d r Acceleration: a = = dt dt2 Here the derivative has its usual definition. For example: dr r(t + Δt) − r(t) = lim . dt Δt→0 Δt As always, a vector equation is three equations, one for each component. Thus ⎛ v = dx /dt⎞ dr ⎜ x ⎟ v = dt means ⎜ vy = dy /dt ⎟ ⎜ ⎟