The acceleration of a ball is given by ( a(x)=-5 k x^{2} ), where ( a ) is acceleration of the ball in ( m / s^{2}, k ) is a constant with unspecified units, and ( x ) is the position of the ball in ( m ). Consider the following initial conditions for position ( x_{0} ) and velocity ( v_{0} ) at ( t=0 s: x_{0}=8 mathrm{~m} v_{0}=2

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The acceleration of a ball is given by  ( a(x)=-5 k x^{2}  ), where  ( a  ) is acceleration of the ball in  ( m / s^{2}, k  ) is a constant with unspecified units, and  ( x  ) is the position of the ball in  ( m  ). Consider the following initial conditions for position  ( x_{0}  ) and velocity  ( v_{0}  ) at  ( t=0 s: x_{0}=8  mathrm{~m} v_{0}=23  mathrm{~m} /  mathrm{s}  ) Use these conditions to detemine the velocity of the ball at  ( x=13  mathrm{~m}  ). You may use  ( k=0.03  ).

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