Find the instantanous velocity

[[Nicolette]]

1. Homework Statement

Find the instantaneous velocity at t=1 by computing v(1)= [h(1+LaTeX Code: \\Delta t)-h(1)]/LaTeX Code: \\Delta t

I found that v(1)= -8ft/sec. Also I know h(1)=24 but i don't understand how to manipulate the h(1+LaTeX Code: \\Delta t) to get the solution.


2. Homework Equations

h(t)=16+24t-16t2


3. The Attempt at a Solution

The solution the teacher gave is v(1)=-8-16tLaTeX Code: \\Delta

 

[Cyosis]

Write out $$\frac{h(1+\Delta t)-h(1)}{\Delta t}$$. The part you have a problem with is probably the $h(1+\Delta t)$ term I will give you a hint. $h(1+\Delta t)=16+24(1+\Delta t)+...$ fill in the rest and work out the brackets.

Note that for an instant of time $\Delta t \rightarrow 0$ so your final answer is correct.

 

[[Nicolette]]

How did you get that h(1+t)=16+24(1+t)?

and when i fill in the rest i get 16+24(1+t)-24 which when worked out would be 16+24t and is not right

 

[Cyosis]

Don't overlook the dots. $h(1+\Delta t)=16+24(1+\Delta t)+...$ my intention was for you to fill in the dots, so basically add the quadratic term to it as well. I hope this is sufficiently clear if not just ask again!

Edit: I just noticed that the same question was asked in the correct introductory physics section. Perhaps a mod could merge this thread with https://www.physicsforums.com/showthread.php?t=305889.