Question

A spaceship accelerates at 150 m/s2 from rest. How long does it take to reach a 1.2 km distant asteroid?

Answer 1

To determine the time it takes for the spaceship to reach the asteroid, we can use the equation of motion:

$d=\frac{1}{2}a{t}^2$

where: d is the distance traveled, a is the acceleration, and t is the time.

In this case, the acceleration is given as 150 m/s^2 and the distance is 1.2 km, which is equal to 1200 meters. We need to convert the distance to meters for consistent units:

$d=1200\text{ meters}$ $a=150{\text{ m/s}}^2$

Now, we can rearrange the equation to solve for time (t):

$t=\sqrt{\frac{2d}{a}}$

Substituting the values:

$t=\sqrt{\frac{2\times 1200}{150}}$ $t=\sqrt{16}$