Explanation

(c) In first case:${\ s}_{1} = ut_{1} + \frac{1}{2}at_{1}^{2}$
$200 = 2u + 2a\ \ \ (\because t_{1} = 2s)$
$u + a = 100$ …(i)
In second case:${\ s}_{2} = ut_{2} + \frac{1}{2}at_{2}^{2}$
420$= 6u + 18a\ \ \ \ \ \ \left( \because t_{2} = 2 + 4 + 6s \right)$
$3a + u = 70\ \ \ \ \ \ \ \ \ \ ...$(ii)
Solving Eqs. (i) and (ii), we get
$a = - 15ms^{- 2}$
and $u = 115cms^{- 1}$
$\therefore\ v = u + at$
$= 115 - 15 \times 7 = 10cms^{- 1}$