1. ## Crazy parametric problem

An object moving along in the xy-plane has position (x(t),y(t)) at t >_ (equal or more than) 0 with dx/dt = 3 + cos(t^2). The derivative of dy/dt is not explicitly given but at t=2, dy/dt = -7. At t=2, the object is at position (1,8)

What is the acceleration vector of the object at t = 4, if, for t >_ (more than or equal) 3, the line tangent to the curve at (x(t),y(t)) has a slope of 2t+1?

No idea how to solve it lol.

2. Originally Posted by Kaitosan
An object moving along in the xy-plane has position (x(t),y(t)) at t >_ (equal or more than) 0 with dx/dt = 3 + cos(t^2). The derivative of dy/dt is not explicitly given but at t=2, dy/dt = -7. At t=2, the object is at position (1,8)

What is the acceleration vector of the object at t = 4, if, for t >_ (more than or equal) 3, the line tangent to the curve at (x(t),y(t)) has a slope of 2t+1?

No idea how to solve it lol.
for $\displaystyle t \geq 3$ , $\displaystyle \frac{dy}{dt} = \frac{dx}{dt}(2t+1)$

get an expression for $\displaystyle \frac{dy}{dt}$, then determine both $\displaystyle \frac{d^2y}{dt^2} = a_y$ and $\displaystyle \frac{d^2x}{dt^2} = a_x$ and evaluate each component at $\displaystyle t = 4$ to determine the acceleration vector.

3. Haha, thanks very much. I didn't realize that I can split a x- or y- derivative from dy/dx. Appreciate it man.