The satellite

The satellite orbiting the Earth at an altitude of 800 km has a speed of 7.46 km/s. How long would it have to move from the start to the orbit to reach this speed if it evenly accelerated its motion in a straight line? What is the acceleration of satellite movement?

Correct answer:

t =  214.4772 s
a =  34.7823 m/s²

Step-by-step explanation:

$$\begin{gathered} s=800\text{km}\to \text{m}=800\cdot 1000\text{m}=800000\text{m} \\ v=7.46\cdot 1000=7460\text{m/s} \\ v=a\cdot t \\ s=\frac{1}{2}\cdot a\cdot t^2 \\ s=\frac{1}{2}\cdot a\cdot (v/a{)}^2 \\ s=\frac{1}{2}\cdot v^2/a \\ a=\frac{v^2}{2\cdot s}=\frac{7460^2}{2\cdot 800000}\doteq 34.7823{\text{m/s}}^2 \\ t=v/a=7460/34.7823=214.4772\text{s} \end{gathered}$$

Try another example