First you need to get position vectors for x and y using polar coordinates:
\(x(t) = 5 cos (\pi t) \\ \\ y(t) = 5 sin (\pi t)\)
Acceleration is the 2nd derivative of position, Find 2nd derivatives of both x and y:
\(x''(t) = -5\pi^2 cos (\pi t) \\ \\ y''(t) = -5\pi^2 sin (\pi t)\)
Finally, evaluate acceleration at (3,4)
x = 3 when cos = 3/5
y = 4 when sin = 4/5
Substitute into acceleration functions:
\(x''(t) = -5\pi^2(\frac{3}{5}) = -3\pi^2 \\ \\ y''(t) = -5\pi^2 (\frac{4}{5}) = -4\pi^2\)
Final Answer:
\(( -3\pi^2 , -4\pi^2)\)
