Astudent is swinging a ball on a string overhead in a horizontal plane. the string initially has length and the ball is moving with an initial speed . the student decides to see how fast they can spin the ball, so they begin moving it faster and faster with a constant tangential acceleration . however, they know that the string is close to breaking, so they decide to keep letting the string get longer and longer in order to keep the tension in the string constant. find expressions for the length of the string and the total acceleration (magnitude and direction) as a function of time, , , and . you may ignore the effect of gravity on the ball.