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 $x=16m$ is

• A. $45J$
• B. $30J$
• C. $70J$
• D. $135J$
• E. $20J$

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 $IJKL$
$W=\left[\frac{1}{2}\times 6\times 10\right]+\left[4\times \left(-5\right)\right]+\left[4\times \left(5\right)\right]+\left[2\times \left(-5\right)\right]$
$=30-20+20-10=20J\cdots \left(i\right)$
According to work energy theorem
$K_f-K_i=W$
or ${\left(K_f\right)}_{x=16m}-{\left(K_i\right)}_{x=0m}=W$
${\left(K_f\right)}_{x=16m}={\left(K_i\right)}_{x=0m}+W$
$=25J+20J$
$=45J$