# Two asteroids bump in space. The larger one has a mass of 3000 kg and the smaller one has a mass of 100 kg. f the force of the collision is 10,000 newtons on each asteroid, what are their accelerations?

Aug 26, 2017

The larger one accelerates at $3.33 \frac{m}{s} ^ 2$ and the other accelerates at $100 \frac{m}{s} ^ 2$

#### Explanation:

The acceleration is obtained thru use of Newton's 2nd Law:
$F = m \cdot a$.
Rearranging this to yield acceleration gives us:
$a = \frac{F}{m}$

Each asteroid experiences a force of 10,000 N. Note, the Newton was defined to be equivalent to $\frac{k g \cdot m}{s} ^ 2$.

The 3000 kg asteroid:
$a = \frac{F}{m} = \frac{10 , 000 N}{3000 k g} = 3.33 \frac{\frac{k g \cdot m}{s} ^ 2}{k g} = 3.33 \frac{m}{s} ^ 2$

The 100 kg asteroid:
$a = \frac{F}{m} = \frac{10 , 000 N}{100 k g} = 100 \frac{\frac{k g \cdot m}{s} ^ 2}{k g} = 100 \frac{m}{s} ^ 2$

Since acceleration is a vector and since the 2 accelerations will be in opposite directions, one of them needs to be negative. Either could be negative depending on assignment of a reference system. The larger one would probably insist on saying his direction is positive, so the smaller asteroid's acceleration would be negative.

I hope this helps,
Steve