Question

a particle starts with a velocity of 2 m/s and moves in a straight line with a retardation of 0.1metre per second square .The first time at which the particle is 15 m from the starting is?

Answer 1

$$\begin{gathered} \mathrm{s}=\mathrm{ut}+\frac{1}{2}{\mathrm{at}}^2 \\ 15=2\mathrm{t}+\frac{1}{2}\times -0.1\times {\mathrm{t}}^2 \\ 15=2\mathrm{t}-0.05{\mathrm{t}}^2 \\ 0.05{\mathrm{t}}^2-2\mathrm{t}+15=0 \\ \mathrm{Solve}\mathrm{the}\mathrm{equation}: \\ \mathrm{t}=10\mathrm{or}30\mathrm{s} \\ \mathbf{Ans}\mathbf{:}\mathbf{}\mathbf{10}\mathbf{}\mathbf{s}\mathbf{}\mathbf{(}\mathbf{first}\mathbf{}\mathbf{time}\mathbf{}\mathbf{to}\mathbf{}\mathbf{reach}\mathbf{}\mathbf{the}\mathbf{}\mathbf{distance}\mathbf{)} \end{gathered}$$