The acceleration vector for the spacecraft Dolphin 163 is given by a(t) = (-2 cos(t), 0,-2 sin(t)). It is also known that the velocity and position att = 0 are (0) = (0, V5, 2) and F(0) = (3, 0,0 ). Assume distances are measured in kilometers (km) and time is measured in seconds (s). (a) Find the position function 7(t) for the spacecraft. (b) Find the function for the speed of the spacecraft and the speed when t = 0. (c) Compute the curvature of the trajectory when t = 0.

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A: Topic :- Calculus

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.