Can someone please help me? 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.

Question

mrnood · Answer

start with the equation
s=3-4t

can you find ds/dt   ?

anonymous · Answer

What is ds?

anonymous · Answer

I know 3 is 0

anonymous · Answer

Can I do s=3-4t
s=0-4t
0=-4t
t=-4

anonymous · Answer

is a derivative always the coefficient of x?

anonymous · Answer

@Asevilla5

asevilla5 · Answer

the derivative of a constant number (like 3) is 0
the derviative of a number times a t (like -4t) is just the number (-4)
since the position function is a straight line, then the velocity will be constant for all time so there will always be a number -4 
for a line you can calculate the slope by using two different points (rise over run)

but a derivative is like moving those two points so close together its like taking the slope of a single point.
since the slope is being taken at a single point, there is no ∆ x like a two point equation (rise/run = ∆y/∆x) so its the slope of a point at a single instant in time

anonymous · Answer

Thank you for that explanation, but i also want to know if the coefficient of x is always the derivative?

anonymous · Answer

velocity is constant, it will be always -4m/sec

anonymous · Answer

ohhh because it's the slope so it will always rise 4 and go left 1?

asnaseer · Answer

@lolabieber - you might find tis useful for understanding derivatives: http://www.mathsisfun.com/calculus/derivatives-introduction.html

anonymous · Answer

okay thank you guys for all your help :) I appreciate it!

asevilla5 · Answer

@lolabieber   yes