A particle has initial velocity $4\hat{i}+4\hat{j}$ ms^-1 and an acceleration $-0.4\hat{i}$ ms^-2, at what time will its speed be 5 ms^-1? 

Since acceleration is in r-direction only, velocity in y-direction will not change. 

When speed = 5 ms^-1

$\begin{array}{l} 5^2={\mathrm{V}}_{\mathrm{x}}^2+{\mathrm{V}}_{\mathrm{y}}^2={\mathrm{V}}_{\mathrm{x}}^2+4^2\\ \Rightarrow {\mathrm{V}}_{\mathrm{x}}=\pm 3{\mathrm{ms}}^{-1}\\ \therefore {\mathrm{V}}_{\mathrm{x}}={\mathrm{u}}_{\mathrm{x}}+{\mathrm{a}}_{\mathrm{x}}\mathrm{t}\Rightarrow \mathrm{t}=\frac{{\mathrm{V}}_{\mathrm{x}}-{\mathrm{u}}_{\mathrm{x}}}{{\mathrm{a}}_{\mathrm{x}}}\\ \mathrm{or} {\mathrm{t}}_1=\frac{3-4}{-0.4}=2.5\mathrm{s}\\ \mathrm{and} {\mathrm{t}}_2=\frac{-3-4}{-0.4}=17.5\mathrm{s}\end{array}$