How Far Does a Rocket Sled Travel with Variable Acceleration?

[eluu]

[SOLVED] Motion Question (Dynamics)

EDIT: I just realized this question was better suited in this forum than the engineering one, sorry :(

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

 

[cristo]

The equations you give only hold for constant acceleration. The acceleration function you give (a=30+2t) is not constant, and so you will need to use calculus to solve even the first part.

 

[eluu]

Ahh whoops, i see it now :)

Now i get the first part with t = 10s and a displacement of 1833.333m

Thanks cristo!

 

[cristo]

Ahh whoops, i see it now :)

Now i get the first part with t = 10s and a displacement of 1833.333m

Thanks cristo!

You're welcome!