Length of acceleration for a rock fragment escaping Mars

[flip290]

Homework Statement

It has been suggested, and not facetiously, that life might have originated on Mars and been carried to Earth when a meteor hit Mars and blasted pieces of rock (perhaps containing primitive life) free of the surface. Astronomers know that many Martian rocks have come to Earth this way. (For information on one of these, search the Internet for “ALH 84001”.) One objection to this idea is that microbes would have to undergo an enormous, lethal acceleration during the impact. Let us investigate how large such an acceleration might be. To escape Mars, rock fragments would have to reach its escape velocity of 5.0 km/s , and this would most likely happen over a distance of about 4.0m during the impact.

a) What would the acceleration in such a rock fragment be?
I got this part! 3.13e6 m/s^2

b) How long would this acceleration last?
This the part I am confused about. I thought it was 0.0016 s but that is incorrect. Any help would be appreciated!

 

[HallsofIvy]

Let the acceleration, in kilometers per second, of the object after after the impact be "a". Then the speed, t seconds after initial impact, is at and the distance moved is (a/2)t^2. We know that the distance is 4m= .004 km so we can solve (a/2)t^2= 4 for t in terms of a. Put that into at= 5 km/s to get an equation for a.

 

[flip290]

Thanks for the reply! I figured out that I actually had the right answer I was just confusing the units.

 

[tvillarrea615]

how did you find part A?

 

[Nickie]

The length of acceleration for a rock fragment escaping Mars would depend on several factors, such as the size and shape of the fragment, the angle of impact, and the composition and density of the Martian surface. Therefore, it is difficult to accurately determine the exact length of acceleration without more specific information.

However, we can estimate the approximate duration of acceleration using the equation for acceleration: a = (vf-vi)/t, where a is the acceleration, vf is the final velocity, vi is the initial velocity, and t is the time.

In this case, the final velocity is the escape velocity of Mars, 5.0 km/s, and the initial velocity is assumed to be 0 m/s. Substituting these values into the equation, we get:

a = (5.0 km/s - 0 m/s)/t

To determine the time, we need to convert the units of velocity from km/s to m/s, which gives us a final velocity of 5000 m/s. Substituting this into the equation, we get:

3.13e6 m/s^2 = (5000 m/s)/t

Solving for t, we get t = 1.6 x 10^-3 seconds, which is the approximate duration of the acceleration. However, as mentioned before, this is just an estimate and the actual length of acceleration may vary.