Question

A particle is acted upon by a force $F$ which varies with position $ x $ as shown in figure. If the particle at $ x=0 $ has kinetic energy of $ 25J, $ then the kinetic energy of the particle at $ x=16\text{ }m $ is

• A. $ 45\text{ }J $
• B. $ 30\text{ }J $
• C. $ 70\text{ }J $
• D. $ 135\text{ }J $
• E. $ 20\text{ }J $

Answer 1

Answer: (A)

Work done $W =$ Area under $F-x$ graph with proper sign $W =$ Area of triangle $ABC +$ Area of rectangle $CDEF +$ Area of rectangle $FGHI +$ Area of rectangle $IJKL$
$W = \left[\frac{1}{2}\times6\times 10\right]+\left[4\times \left(-5\right)\right]+\left[4\times \left(5\right)\right]+\left[2\times \left(-5\right)\right]$
$= 30 -20 + 20 - 10 = 20\, J \quad\cdots \left(i\right)$
According to work energy theorem
$K_{f}-K_{i} = W$
or $\left(K_{f }\right)_{x = 16\, m} - \left( K _{i} \right)_{x = 0 \,m} = W$
$\left(K_{f }\right)_{x = 16\, m} = \left( K _{i} \right)_{x = 0 \,m}+W$
$= 25\,J+20\,J$
$= 45\,J$