Question

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

Answer 1

Answer:

-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.