#### Transcript of The Calculus of a Marathon

**The Calculus of Running a Marathon**

design by Dóri Sirály for Prezi

Used by many runners

We know it shows location but...

how does it work?

demo

How Can Calculus Help You Win Your Marathon?

Let's Find Out!

Runner A Calculations

Global Positioning System

Runner A: a = 3 cos(x) + 1

Runner B: a = x/20

Pre-race info:

Both runners start out with a velocity of 0

Runner B oversleeps and comes late to the race, starting the race 200 meters behind the start line

And They're Off!

V = 3 sin(x) + x

X = 3 sin(x) + x dx

X = -3 cos(x) + x^2/2 + c

0 = -3 cos(0) + 0 + c

0 = -3 + c

C = 3

X = -3 cos(x) + x^2/2 +3

A = 3 cos(x) + 1

V = 3 cos(x) + 1 dx

V = 3 sin(x) + x + c

0 = 3 sin(0) + 0 + c

c = 0

V = 3 sin(x) + x

Runner B Calculations

V = 1/40 x^2

X = 1/40 x^2 dx

X = 1/120 x^3 + c

-200 = 1/120 (0)^3 + c

c = -200

X = 1/120 x^3 - 200

A = x/20

V = x/20 dx

V = 1/40 x^2 + c

0 = 1/40 (0)^2 + c

c = 0

V = 1/40 x^2

When Will Runner A Finish?

42, 195 =

-3 cos(x) + x^2/2 +3

0 = -3 cos(x) + x^2/2 – 42, 192

t = 290.49 minutes to finish the marathon

That is close to 5 hours

Marathon = 26.2 miles

26.2 mi = 42, 195 m

To find time it takes to finish the race, we can plug 42, 195 in for X and solve for (x), or time in minutes

When Will Runner B Finish?

42, 195 = 1/120 x^3 – 200

42, 395 = 1/120 x^3

t = 171.99 minutes to finish the marathon

That is close to 3 hours

Marathon = 26.2 miles

26.2 mi = 42, 195 m

To find time it takes to finish the race, we can plug 42, 195 in for X and solve for (x), or time in minutes

Full transcript