Physics

Problem

0.5\,\text{kg}

block slides on a smooth horizontal surface. It is acted on by a position–dependent force

F(x)=20e^{-0.5x}\,\text{N}

directed along the positive

x

–axis. The block is released from rest at

x=0

. a. (i) Obtain an expression for the work done on the block as a function of its displacement

x

. b. (ii) Calculate the displacement required for the block to gain

3\,\text{J}

of kinetic energy. c. (iii) If instead the block were pulled from

x=3\,\text{m}

back to

x=0

, state with reason whether the work done by the given force would be positive, negative, or zero.