C Roettger, Fall 14 Math 265 Quiz 4C – Solutions Problem 1 A particle is traveling on a curve with position at time t given as r(t) = 5 sin(t)i + 3tj. a) Find the velocity and acceleration vectors. b) Find the unit tangent vector T and the unit normal vector N at time t = π/2. Solution. For a), v = 5 cos(t)i + 3j a = −5 sin(t)i For b), T = j for t = π/2 and N = −i. We know that N is orthogonal to N, so it is a multiple of i. It has length 1, so it is ±i. Finally, it points to the same side of the tangent line as the curve, so it has to be −i (see graph below). Alternatively, N points to the same side of the tangent line as a. This is much easier than computing dT /dt.