## University Physics with Modern Physics (14th Edition)

(a) The greatest speed the mass reaches is 3.03 m/s when the spring has reached its normal length. This occurs after the block moves a distance of 9.59 cm (b) The greatest acceleration of the mass is $95.9~m/s^2$ and this occurs when the mass is initially released from rest.
(a) We can find the distance x that the spring is compressed. $\frac{1}{2}kx^2 = 11.5~J$ $x^2 = \frac{23~J}{2500~N/m}$ $x = \sqrt{\frac{23~J}{2500~N/m}}$ $x = 0.0959~m$ We can find the greatest speed the mass reaches. $\frac{1}{2}mv^2 = 11.5~J$ $v^2 = \frac{23~J}{2.50~kg}$ $v = \sqrt{\frac{23~J}{2.50~kg}}$ $v = 3.03~m/s$ The greatest speed the mass reaches is 3.03 m/s when the spring has reached its normal length. This occurs after the block moves a distance of 9.59 cm (b) The greatest acceleration occurs when the spring pushes with its greatest force. This occurs when the block is released from rest. $ma = kx$ $a = \frac{kx}{m} = \frac{(2500~N/m)(0.0959~m)}{2.50~kg}$ $a = 95.9~m/s^2$ The greatest acceleration of the mass is $95.9~m/s^2$ and this occurs when the mass is initially released from rest.