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

@Mertsj

Answer 2

@Brandon77

Answer 3

Did you see my comments on the other question about taking the derivative

Answer 4

So it's -4..?

Answer 5

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)

Answer 6

and so yes thats right

Answer 7

So when t=8..?

Answer 8

since the position function is a straight line, then the velocity will be constant for all time

Answer 9

so it will always be -4

Answer 10

So what exactly is a derivative in definition? I'm sure you can explain it better than some websites :P

Answer 11

okay. for a line you can calculate the slope by using two different points (rise over run)

but a dervative is like moving those two points so close together its like taking the slope of a single point.

Answer 12

derivative*

Answer 13

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