find time to reach 100m given only acceleration

[Josh K]

I am really struggling with a Dynamics homework problem and I can't figure out where I'm going wrong. The problem is:

The acceleration of a rocket traveling upward is given by a = (6 + 0.02s) m/s^2, where s is in meters. Determine the time needed for the rocket to reach an altitude of s = 100m. Initially, v = 0m/s and s = 0m when t = 0s.
Answer from the back of the book is t = 5.62 s

I had asked a tutor for help and got a super complicated walk through that I can't fully understand. I have attached my current attempt including the formula the book gives for the integral used at dt=ds/v.

I tried using integral-calculator.com and came up with the right answer but the page doesn't show work. Here is a link to that calculation: http://www.integral-calculator.com/#expr=1/(sqrt(12x+0.02x^2))&lbound=0&ubound=100

 

[Deleted member 4993]

I am really struggling with a Dynamics homework problem and I can't figure out where I'm going wrong. The problem is:

The acceleration of a rocket traveling upward is given by a = (6 + 0.02s) m/s^2, where s is in meters. Determine the time needed for the rocket to reach an altitude of s = 100m. Initially, v = 0m/s and s = 0m when t = 0s.
Answer from the back of the book is t = 5.62 s

I had asked a tutor for help and got a super complicated walk through that I can't fully understand. I have attached my current attempt including the formula the book gives for the integral used at dt=ds/v.

I tried using integral-calculator.com and came up with the right answer but the page doesn't show work. Here is a link to that calculation: http://www.integral-calculator.com/#expr=1/(sqrt(12x+0.02x^2))&lbound=0&ubound=100

Check the integral of a ds

 

[Josh K]

Thanks. I figured out where my problem was occurring. I was plugging 12 / 2 sqrt(0.02) into my calculator which it was reading as (12 / 2) sqrt(0.02) when I wanted it to read 12 / (sqrt(0.02)). The first equation gave me 0.8 something where the latter came out to be 42.426... I kept plugging it in wrong so I kept getting the wrong answer but, when I finally figured that out, the rest of the problem worked out just fine.

 

[Ishuda]

I am really struggling with a Dynamics homework problem and I can't figure out where I'm going wrong. The problem is:

The acceleration of a rocket traveling upward is given by a = (6 + 0.02s) m/s^2, where s is in meters. Determine the time needed for the rocket to reach an altitude of s = 100m. Initially, v = 0m/s and s = 0m when t = 0s.
Answer from the back of the book is t = 5.62 s

I had asked a tutor for help and got a super complicated walk through that I can't fully understand. I have attached my current attempt including the formula the book gives for the integral used at dt=ds/v.

I tried using integral-calculator.com and came up with the right answer but the page doesn't show work. Here is a link to that calculation: http://www.integral-calculator.com/#expr=1/(sqrt(12x+0.02x^2))&lbound=0&ubound=100

Well, for what it's worth, I agree with the answer from the back of the book. If you have studied second order differential equations, I think a much easier way to approach the problem would be to note that
a(t) = \(\displaystyle \frac{d^2 s(t)}{d t^2}\) = .02 s(t) + 6
or
\(\displaystyle \frac{d^2 s}{d t^2}\, -\, 0.02\, s\) = 6
and go from there.