Question

Write a in the form a = aₜT + aₙN at the given value of t without finding T and N. r(t) = (2t + 4)t + (t) J + (t²)k, t= - 1 a = T + N

Answer 1

The response addresses the student's request to write the acceleration vector a in the form a = aₜtT + aₙN for a vector function r(t) at a specific value of t without finding the unit vectors T and N.

Step-by-step explanation:

The question asks to write acceleration, a, in the form of a = aₜtT + aₙN for a given vector function r(t) and a specific value of t.

It appears that the student is supposed to use the fundamental kinematic equation and vector calculus without actually finding the tangential unit vector T and the normal unit vector N.

We are examining motion along a path described by r(t) at the given time t = -1. The specific kinematic equation provided does not directly apply to vector functions, but suggests that an initial value wo (initial velocity or angular velocity) is zero, leading to the simplified formula w = wo + at.

However, this equation relates more to motion in a straight line or rotational motion with constant acceleration, and may be a misdirection in the context of the vector function given.

Given the vector function in the question, we should normally find the derivative of r(t), which gives us velocity, and then the second derivative to obtain acceleration.

However, since the components of the vectors T and N are not to be found, and only the equation structure is required, the usual process may need to be altered or simplified for the solution.