A block of mass lies on a smooth horizontal surface

PHYSICS · Multi-part · AP · Physics C: Mechanics · Work Energy and Power · Work Energy and Power

Problem

A block of mass

2\,\text{kg}

lies on a smooth horizontal surface. A variable horizontal force given by

F(x)=4+2x\;\text{N}

(where

x

is in metres) acts on the block, starting from

x=0

. The block is initially at rest. (i) Find the work done by the force as the block moves from

x=0

x=3\,\text{m}

. (ii) Calculate the speed acquired by the block at

x=3\,\text{m}

. (iii) If the same force continued to act beyond

x=3\,\text{m}

, at what displacement from the start would the block’s speed reach

10\,\text{m}\,\text{s}^{-1}

? (Give your answer correct to one decimal place.)