Explanation:
Here, \(m = 5\,kg,\,\vec F = ( - 3\hat i + 4\hat j)N\)
Initial velocity at \(t = 0,u = (6\hat i - 12\hat j)\)
Retardation, \(a = \frac{F}{m}\)
\( = \left( { - \frac{{3\hat i}}{5} + \frac{{4\hat i}}{5}} \right)\,\,m/{s^2}\)
As final velocity is along \(Y\)-axis, its \(x\)-component must be zero.
From \({v_x} = {u_x} + {a_x}t\), for \(X\) -component only,
\(0 = 6\hat i - \frac{{3\hat i}}{5}t\)
\(t = \frac{{5 \times 6}}{3} = 10\,s\)