MATH 1172 Midterm: MATH 1172 Ohio State University Math 1172 12.7 Solutions Fa 2014

• School: Ohio State University
• Department: Mathematics
• Course: MATH 1172
• Professor: All

Document Summary

November 18, 2015: consider the position function of an object: r(t) = h3 cos(2 t), 3 sin(2 t)i , for 0 t 1. Find the velocity, speed, and acceleration function of the object. Solution: once one remembers the follow- ing relations the problem reduces to taking the derivative of simple trig functions and nding the magnitude of vector valued functions: v(t) = r (t) s(t) = |v(t)| a(t) = v (t). By taking the derivative in each coordinate, v(t) = h 6 sin(2 t), 6 cos(2 t)i, and v(t) = h 12 2 cos(2 t), 12 2 sin(2 t)i. Taking the magnitude of the velocity vector gives: s(t) =p( 6 sin(2 t))2 + (6 cos(2 t))2 = 6 : consider the position functions: r(t) = he 2t + 1, et e ti. R(t) = ht2 + 1, t t 1i.