Question

A ball spins on a 0.5m-long string with a speed of 3.8m/s. Calculate the acceleration of the ball.

Answer 1

v^2/R

Answer 2

or are you supposed to derive centripetal acceleration?
s = speed
w = angular velocity = s/r radians/s
V = velocity vector = Vx i + Vy j
Vx = s cos theta
Vy = s sin theta
theta = w t
V = s cos wt i + s sin w t j
A = dV/dt
A= -s w sin w t i + s w cos w t j
but w = s/r
A = -s^2/r sin wt i + s^2/r cos w t
|A| = s^2/r sqrt(sin^2+cos^2)
= s^2/r
if you look at the direction of the acceleration, it is toward the origin :)