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 a distant asteroid, we can use the kinematic equation:

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

where:

• $d$ is the distance traveled,
• $u$ is the initial velocity (which is zero in this case as the spaceship starts from rest),
• $a$ is the acceleration, and
• $t$ is the time.

In this case, the spaceship's acceleration is given as $a=150{\text{m/s}}^2$ and the distance to the asteroid is $d=1.2\text{km}=1200\text{m}$.

Plugging these values into the equation, we get:

$1200=0\cdot t+\frac{1}{2}\cdot 150\cdot t^2$

Simplifying the equation, we have:

$1200=75t^2$

Dividing both sides by 75, we get:

16=t2<annotation e