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eluu
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Homework Statement
The rocket sled starts from rest and accelerates at a = 30 + 2t until its velocity is 400m/s. It then hits a water brake and its acceleration is a = -0.003v^2 m/s^2 until its velocity decreases to 100 m/s. What total distance does it travel?
Homework Equations
v = u + at
s = ut + at^2/2
v^2 = u^2 + 2as
The Attempt at a Solution
I'm pretty sure my first part is correct but here it is anyway:
v = u + at
v = u + (30 + 2t)t
*Sub in values and i get t = 8.508s, then i get s = 1701.652m from the other equation
For the next part I've done this:
a = -0.003v^2
v dv/dx = -0.003v^2
dv/v = -0.003dx *integrate both sides
ln(v) = -0.003x + C
when v = 400, x = 0, C = ln(400)
ln(v) = -0.003x + ln(400)
so when v = 100, i get x = 462.098m
So the total distance i get is 2163.750m but the answer says 2300m...
Where did i go wrong or is the answer given incorrect? :S