Finding Acceleration: Solving a Simple Velocity Equation at 0.5s

[The Matador]

Homework Statement

Velocity in m/s at time t is defined as v= 20t(1+2t)^-2

Find Acceleration at 0.5s

2. The attempt at a solution

I missed the day we covered this topic in class and I am under the assumption that I would find the derivative of 20t(1+2t)^-2 and then find the derivative once more to get acceleration. Once I get the second derivative its as easy as substituting 0.5 for t. Unfortunately I never get the correct answer which I was told is 9.6m/s. Is the answer wrong? I end up with 15m/s all the time.

 

[hage567]

If you are given the velocity function you only need to differentiate once to get the acceleration.

 

[The Matador]

I must be doing something wrong I keep getting the wrong answers.

Example:

s(t) = (4t^2 + 5)^3 t=1

I do the work

First Derivative - 24t(4t^2 + 5)^2
Second Derivative - 384t^2(4t^2 + 5)

My answer is 3456 m/s and the book tells me it is 5400 m/s

 

[hage567]

So is this supposed to be a new question? What happened with the first one you posted?

Note the unit of acceleration is m/s^2.

Your second derivative is not right. You're using the product rule, right? You're missing a term.

 

[The Matador]

I feel really stupid right now. I knew something was up, turns out I was forgetting the product rule for all the questions. Thanks for clueing me into that. What a silly mistake.

 

[hage567]

You're welcome, lol. Those things happen.