Final answer:
To find t(t), substitute the given value of t into the equation for r(t). To find n(t), find the unit vector in the direction of the tangent to the curve at t = 2. To find at and an, find the derivative of the velocity vector v(t).
Step-by-step explanation:
To find t(t), we can substitute the given value of t into the equation for r(t). t(t) = 2i + 5j.
To find n(t), we need to find the unit vector in the direction of the tangent to the curve at t = 2. Since the tangent vector is parallel to the velocity vector, we can find the velocity vector by taking the derivative of r(t). v(t) = r'(t) = i + 5j. Now, we can find the unit vector n(t) by dividing the velocity vector v(t) by its magnitude. n(t) = (1/√26)i + (5/√26)j.
To find at, we need to find the derivative of the velocity vector v(t). a(t) = v'(t) = 0i + 0j = 0.
To find an, we need to find the dot product of the acceleration vector a(t) and the unit vector n(t). Since the acceleration vector is zero, the dot product is also zero. an = a(t) · n(t) = 0.