Answer to Question #323933 in Mechanics | Relativity for Ismaila Bashiru

Question

In a space 5.82 x 1000000kg rocket experiences a constant force of 6.94 x 1000000000N in the direction of its movement. At time t = 0s,it flies past a planet at a velocity of 57.2m/s. How far away is the rocket from the planet when t = 25.4s?

Answer 1

The distance, covered by rocket in time t, is

$s=v_0t+\frac{at^2}{2},$

where $v_0$ - the initial speed;

a - the acceleration.

From Newton's 2nd law:

$F=ma,\newline a=\frac{F}{m},$

where F - force, experienced by the rocket.

So,

$s=v_0t+\frac{Ft^2}{2m}=57.2\cdot 25.4+\frac{6.94\cdot 10^9\cdot 25.4^2}{2\cdot 5.82\cdot 10^6}=3.86\cdot10^5\space m.$