Kinematic Problem: Tangential Acceleration and Radius of Curvature at t=1

[Dell]

a body moves according to the following:
a_y=2-4t
a_x=-1
v_y=2t-2t²
v^x=1-t
x₀=2
y₀=3

what is the tangential acceleration when t=1?
what is the radius of curvature of the motion when t=1?

a_T=$$\vec{a}$$dot$$\vec{v}$$/|v|
at t=1, $$\vec{v}$$=0 so there is no tangential acceleration, how can this be true?

the secon part of the question is also not making sence

a_r=v²/r, but here v=0 and ar=3 since there is no a_T and ax=-1, ay=-2?

 

[LowlyPion]

I think what the question is asking is what is the linear acceleration at t=1 given by the expression of the acceleration vector at that time. Isn't this merely a matter of evaluating the a_(t) function at t=1?

For the radius of curvature, I would suggest:
http://www.intmath.com/Applications-differentiation/8_Radius_curvature.php

 

[thomate1]

I would like to clarify and provide a response to the given kinematic problem. First of all, the given problem does not provide enough information to accurately determine the tangential acceleration and radius of curvature at t=1. In order to solve for these values, we would need to know the position, velocity, and acceleration of the body at t=1.

Furthermore, the given equations for ay and ax do not match the given initial conditions of x0=2 and y0=3. This suggests that there may be errors or missing information in the given problem.

Assuming that the initial conditions are correct and the equations for ay and ax are meant to represent the acceleration components, we can solve for the tangential acceleration and radius of curvature at t=1 using the equations aT=\vec{a}\cdot\vec{v}/|v| and ar=v^2/r.

At t=1, the velocity components are vx=0 and vy=0, so the magnitude of the velocity, |v|, is also equal to 0. This means that the tangential acceleration, aT, cannot be determined using the given information.

Similarly, the radius of curvature, r, cannot be determined without knowing the velocity and acceleration components at t=1. As mentioned before, the given equations for ay and ax do not match the initial conditions, so it is not possible to accurately determine the radius of curvature at t=1.

In conclusion, the given kinematic problem does not provide enough information to accurately determine the tangential acceleration and radius of curvature at t=1. It is possible that there are errors or missing information in the given problem. Further clarification or additional information is needed to solve for these values.