The position of an object at time t is given by s(t) = 1 - 10t. find the instantaneous velocity at t = 10 by finding the derivative.

i know i have to use the differential quotient formula:
f(x-h) - f(x) / h

The instantaneous velocity at is 10.

The instantaneous Velocity of the object at a time is determined by mathematical concept of Derivative, whose description is shown below:

(1)

Where:

- Time difference.

- Function position evaluated at time .

If we know that , then the instantaneous Velocity of the object is:

As instantaneous velocity is a constant function, it means that objects travels at constant velocity. Hence, we conclude that the instantaneous velocity at is 10.

Please see this question related to instantaneous Velocity: link

-10

Step-by-step explanation:

Velocity is the derivative of position.  Derivative is defined as:

f'(x) = lim(h->0) [ f(x+h) - f(x) ] / h

s(t) = 1 - 10t

s(t+h) = 1 - 10(t+h)

Plugging in:

s'(t) = lim(h->0) [ 1 - 10(t+h) - (1 - 10t) ] / h

s'(t) = lim(h->0) (1 - 10t - 10h - 1 + 10t) / h

s'(t) = lim(h->0) (-10h) / h

s'(t) = lim(h->0) -10

s'(t) = -10

v(t) = -10

So at t=0, v(0) = -10.