A particle is travelling along a circular curve with radius 20m. It has an initial speed of 22m/s and then begins to decrease its speed at a rate of a=(-0.25s) m/s2. Determine the magnitude of the acceleration of the particle two seconds later.
x2 + y2 = R2
The Attempt at a Solution
I integrated the acceleration with respect to s and then set that equal to ds/dt.
ds/dt = -0.125s2
Then I moved things around so I had ds/s2 = -0.125dt and integrated both sides. I then end up with a final solution of s=8/t, which i took the derivative of to get velocity, v = -8/t2 and took the derivative again to get acceleration, a = 16/t3. Then I took the original velocity 22m/s and subtracted the velocity found using the above equation, and used this final velocity to find the centripetal acceleration. Then I used the above equation for acceleration to find the component of the acceleration perpendicular to the radius, squared this and added it to the square of the centripetal acceleration, took the square root and well... got the wrong answer. Help?