Question

Two rockets having the same acceleration start from rest, but the first rocket travels for twice as much time as the second one. If rocket A goes for 310 km, how far will B go? If rocket A reaches a speed of 320 , what speed will rocket B reach?

Answer 1

Let ta be the time the first rocket travels and tb be the time the second rocket travels. ta = 2tb
We apply:
sa = ut + 1/2 at², with u = 0 since they start from rest. 
310000 = 1/2a(ta)²
a = 620000 / 4(tb)²

sb = 1/2 a(tb)²
sb = 1/2 x 620000 / 4(tb)² x (tb)²
sb = 77.5 Km

We apply v = u + at, with u = 0
va = a(ta)
a = 320/2(tb)

vb = a(tb)
vb = (320/2tb)(tb)
vb = 160