Question

a rocket, initially at rest, steadily gains speed for 3.10s while traveling upwards 30.0m.
what was the rockets final speed?

Explanation:

Step1: List known variables

Initial velocity $v_0 = 0\ \text{m/s}$, time $t = 3.10\ \text{s}$, displacement $s = 30.0\ \text{m}$

Step2: Use kinematic displacement formula

$$s = \frac{(v_0 + v_f)}{2}t$$

Step3: Solve for final speed $v_f$

Rearrange formula: $v_f = \frac{2s}{t} - v_0$
Substitute values: $v_f = \frac{2\times30.0}{3.10} - 0$
Calculate: $v_f = \frac{60.0}{3.10} \approx 19.35\ \text{m/s}$

Answer:

19.4 m/s (rounded to 3 significant figures)