Engineering Dynamics (Motion related)

[eluu]

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]

Duplicate post: see here https://www.physicsforums.com/showthread.php?t=192746

 

[piercas]

Your calculations for the first part seem to be correct. However, for the second part, you have integrated incorrectly. Instead of integrating both sides, you should only integrate the left side, as the right side is a constant (since x is the distance traveled, it is not a function of v). So the correct integration would be:

∫dv/v = ∫-0.003dx

ln(v) = -0.003x + C

When v = 400, x = 0, so C = ln(400)

ln(v) = -0.003x + ln(400)

When v = 100, x = 462.098m, so the total distance traveled is 1701.652 + 462.098 = 2163.750m. Your answer is correct. It is possible that the answer given is incorrect, or there may have been a mistake in the calculation.