MATH 222 Midterm: MATH 222 KSU Test 1f97
15 Feb 2019
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To receive credit you must show your work. (25) 1. An object is moving in 3-space according to the parametric equations x = cos t , y = sin t and z = 3 sin t where t is the time in seconds. Find, as functions of t : position vector ~r , velocity vector ~v , acceleration vector ~a , speed ds dt, tangential component of acceleration at , curvature = Its acceleration vector as a function of time is ~a = (sin t)~i 3~j . Suppose that at t = 0 its velocity vector is. ~v(0) = ~j and its position vector is ~r(0) = ~i ~j . Find the velocity vector and the position vector as functions of t . Then write the parametric equations for the motion. Suppose you know that at t = 2 seconds the position vector is ~r(2) = 2~i + ~j ~k , the velocity vector is.
