Aparticle moves around the circle x^2 + y^2 = 25 at constant speed, making one revolution in 2 seconds. find the acceleration vector when it is at (3, 4).

First you need to get position vectors for x and y using polar coordinates:


Acceleration is the 2nd derivative of position, Find 2nd derivatives of both x and y:


Finally, evaluate acceleration at (3,4)
x = 3 when cos = 3/5
y = 4 when sin = 4/5
Substitute into acceleration functions:


Final

The answer is