Two points $A$ and $B$ move from rest along a straight line with constant acceleration $f$ and $f$ '…
Two points $A$ and $B$ move from rest along a straight line with constant acceleration $f$ and $f$ ' respectively. If $A$ takes $m$ sec. more than $B$ and describes ' $n$ ' units more than $B$ in acquiring the same speed then
$\left(f^{\prime}-f\right) n=\frac{1}{2} f f^{\prime} m^2$
Solution
$
\begin{aligned}
& v^2=2 f(d+n)=2 f^{\prime} d \\
& v=f^{\prime}(t)=(m+t) f
\end{aligned}
$
eliminate $d$ and $m$ we get
$
\left(f^{\prime}-f\right) n=\frac{1}{2} f f^{\prime} m^2 \text {. }
$