Super Soldier Speed Test

Calculus Level 3

Scientists in a lab have developed a new super soldier, one that can go up to unfathomable speeds!

During a speed test, the soldier went haywire and escaped into the wild. Oh no!

Fortunately, we recovered the measurements of its velocity over time. After going over it, we discovered that the plotted data looked incredibly similar to:

$v(t) = \sum_{n=0}^{\infty}t^n$ where $v(t)$ is the velocity in km/s and $t$ is time.

Given that this function $v(t)$ is the real function for the velocity of the super soldier, what distance did it travel over half a second in meters?

The answer is 693.1471805599453.

1 solution

A Former Brilliant Member
Jun 10, 2020

For $t<1, v(t)=\dfrac{1}{1-t}\implies s=\displaystyle \int_0^t \dfrac{dt}{1-t}=\displaystyle \ln |\frac{1}{1-t}|$ .

For $t=\dfrac{1}{2},s=\ln 2=0.693147...$ km. $=\boxed {693.14718...}$ m.

blecch, unit conversion :(

Richard Desper - 1 year ago

gotta be careful ;)

James Watson - 1 year ago

Super Soldier Speed Test

The answer is 693.1471805599453.

1 solution

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