Explanation

(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 $IJKL$
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$W = \left\lbrack \frac{1}{2}\ \times 6 \times 10 \right\rbrack + \left\lbrack 4 \times ( - 5) \right\rbrack + \lbrack 4 \times 5\rbrack + \left\lbrack 2 \times ( - 5) \right\rbrack$
$\Rightarrow W = 30 - 20 + 20 - 10 = 20\ J$ ….(i)
According to work energy theorem
$K_{f} - K_{i} = W \Rightarrow \left( K_{f} \right)_{x = 16m} - \left( K_{i} \right)_{x = 0m} = W$
$\left( K_{f} \right)_{x = 16m} = \left( K_{i} \right)_{x = 0m} + W$
$= 25\ J + 20\ J = 45\ J$ [Using (i)]