c
Consider the given expression.

\(F =\left(100-0.5 \times 10^{5} t \right) N\)

Given that, \(F =0\)

\(\left(100-0.5 \times 10^{5} t \right)=0\)

\(t =\frac{100}{0.5 \times 10^{5}}\)

\(=2 \times 10^{-3} sec\)

Calculate the impulse as,

\(I =\int Fdt\)

\(=\int\left(100-0.5 \times 10^{5} t \right) dt\)

\(=\left[100 t -\frac{10^{5}}{2} \frac{ t ^{2}}{2}\right]\)

\(=\left[100\left(2 \times 10^{-3}\right)-\frac{10^{5}}{2} \frac{\left(2 \times 10^{-3}\right)^{2}}{2}\right]\)

\(=0.1 Ns\)