Answer:
[tex]35.0\; \rm m \cdot s^{-1}[/tex].
Explanation:
The question states that the rocket gains speed steadily. In other words, the acceleration of this rocket in that four seconds would be constant.
Using information from the question:
Apply the SUVAT equation [tex]\displaystyle \frac{1}{2}\, a \cdot t^{2} + v_{0}\cdot t = x[/tex] to find [tex]a[/tex], the acceleration of this rocket.
[tex]\displaystyle \frac{1}{2}\, a \times (4.00\; {\rm s})^{2} + 0 = 70.0\; \rm m[/tex].
[tex]\begin{aligned}a &= \frac{70.0\; \rm m}{\displaystyle \frac{1}{2} \times (4.00\; {\rm s})^{2}} = 8.75\; \rm m \cdot s^{-2}\end{aligned}[/tex].
In other words, this rocket accelerated from rest at a constant [tex]a = 8.75\; \rm m \cdot s^{-2}[/tex] for [tex]t = 4.00\; \rm s[/tex]. The final velocity of this rocket would be:
[tex]\begin{aligned}& v_{0} + a\cdot t \\ =\; & 0 \; \rm m\cdot s^{-1} + 8.75\; \rm m\cdot s^{-2} \times 4.00\; \rm s \\ =\; & 35.0\; \rm m\cdot s^{-1}\end{aligned}[/tex].
