Question

The position of an object at time t is given by s(t) = 3 - 4t. Find the instantaneous velocity at t = 8 by finding the derivative.

Answer 1

@jim_thompson5910 @Loser66

Answer 2

@phi

Answer 3

did you find the derivative of s(t) with respect to t ?

Answer 4

I still don't really understand how you find the derivative. What I got so far: Using the general formula f'(a)=lim h->0 [f(a+h)-f(a)]/h, f'(8)=lim t->0 [f(8+t)-f(8)]/t, f'(8)=lim t->0 [3-4(t+8)-(3-4t)]/t=lim t->0 (3-4t-32-3+12t)/t=lim t->0 (8t-32)/t

Answer 5

"Using the general formula f'(a)=lim h->0 [f(a+h)-f(a)]/h, s'(8)=lim t->0 [s(8+t)-s(8)]/t, s'(8)=lim t->0 [3-4(t+8)-(3-4t)]/t=lim t->0 (3-4t-32-3+12t)/t=lim t->0 (8t-32)/t=lim t->0 "

Answer 6

I got stuck in the process of finding the derivative.

Answer 7

the general formula for the derivative is
\[\lim_{h \rightarrow 0}\frac{ 3-4(t+h)- (3-4t) }{ h }\]

Answer 8

Then plug in 8 for t?

Answer 9

that gives you
\[\lim_{h \rightarrow 0}\frac{3-4t-4h-3+4t}{h}= \lim_{h \rightarrow 0}\frac{-4h}{h}= -4\]

Answer 10

that says that the velocity is a constant -4, independent of time

Answer 11

see
http://www.khanacademy.org/math/calculus/differential-calculus/derivative_intro/v/calculus--derivatives-1--new-hd-version

for more info on how to do derivatives