Question

A body travels a distance $s$ in $t$ seconds. It starts from rest and ends at rest. In the first part of the journey, it move with constant acceleration $f$ and in the seconds part with constant retardation $r$. The value of $t$ given by

• A. $2s(\frac{1}{f}+\frac{1}{r})$
• B. $\frac{2s}{\frac{1}{f}+\frac{1}{r}}$
• C. $\sqrt{2s(f+r)}$
• D. $\sqrt{2s\left(\frac{1}{f+r}\right)}$

Answer 1

Answer: (D)

$\sqrt{2s\left(\frac{1}{f+r}\right)}$

let first part be $t_1$ and second part be $t_2$

$D_1=ut+\frac{1}{2}a{t}^2=\frac{f{t}_1^2}{2}$

for $D_2$, $v=0$,$a=-\mu$

$D_2={r{t}_2}^2-\frac{{r{t}_2}^2}{2}=\frac{{r{t}_2}^2}{2}{D}_1+D_2=S,t_1=t_2=\frac{t}{2}\frac{f{t_1}^2}{2}+\frac{{r{t}_2}^2}{2}=S{t_1}^2=\frac{2S}{f+r},t=\sqrt{\frac{2S}{f+r}}$