Question

The position of an object at time t is given by s(t) = 1 - 12t. Find the instantaneous velocity at t = 2 by finding the derivative.

Answer 1

Answer:

The velocity of the object at t=2 is 12m/s in opposite direction.

Step-by-step explanation:

The given function is

$s(t)=1-12t$

Differentiate with respect to time.

$s'(t)=0-12(1)$

We know the change in displacement with respect to time is known as velocity.

$v(t)=-12$

It is a constant function. So, the velocity of object is same for any value t.

At t=2,

$v(2)=-12$

Negative sign represents the velocity in opposite direction.

Therefore the velocity of the object at t=2 is 12m/s in opposite direction.

Answer 2

s(t) = 1 - 12t
s'(t)= -12 

As you can see the derivative is a constant, this is because the function is linear. 
The velocity of a linear function is constant so at t=2 it is -12. (at any t would be the same)