Answer
The time it takes the rock to reach a velocity of $27.8m/s$ on Mars is approximately $7.473$ seconds and on Jupiter is approximately $1.215$ seconds.
Work Step by Step
1) On Mars: $$s(t)=1.86t^2$$
- Velocity: $v(t)=\frac{ds}{dt}=(1.86t^2)'=3.72t$
The time it takes for $v(t)$ to reach $27.8m/s$ is $$3.72t=27.8$$
$$t\approx7.473s$$
2) On Jupiter: $$s(t)=11.44t^2$$
- Velocity: $v(t)=\frac{ds}{dt}=(11.44t^2)'=22.88t$
The time it takes for $v(t)$ to reach $27.8m/s$ is $$22.88t=27.8$$
$$t\approx1.215s$$
