Question

A train starts from station A with a uniform acceleration $a_1$ for some distance and then goes with uniform retardation $a_2$ for some more distance to come to rest at station B. The distance between stations A and B is 4 km and the train takes 1/15 h to complete this journey. If accelerations are
in km per minute, find value of $\frac{1}{a_1}+\frac{1}{a_2}$.

Answer 1

$S_1=u_1{t}_1+\frac{1}{2}{a}_1{t}_1^2\Rightarrow \because u=0$ and $a=\frac{v}{t}$

$S_1=\frac{1}{2}{V}_1{t}_1...\left(i\right)$ $V_1=V_2$

$S_2=u_2{t}_2-\frac{1}{2}{a}_2{t}_2^2$

$=\frac{1}{2}{v}_2{t}_2$

$S=S_1+S_2=\frac{1}{2}V(t_1+t_2)$

$\because t_1=t_2$

$S=\frac{1}{2}V\left(2t_1\right)$

$4000=\frac{1}{2}\times v\times h\times 60$

$v=33.33m/s.$

Now $=\frac{1}{a_1}+\frac{1}{a_2}=\frac{t_1}{v_1}+\frac{t_2}{v_1}=7.2$