Question

The position of an object at time t is given by s(t) = -2 - 6t. Find the instantaneous velocity at t = 2 by finding the derivative.

Answer 1

bearing in mind that the derivative of s(t) is s'(t) = velocity, thus

`\bf s(t)=-2-6t\implies \left. \cfrac{ds}{dt}=-6 \right|_(t=2)\implies -6`

namely a negative rate, so the object is slowing down to a stop.

Answer 2

the instantaneous velocity at t = 2 is -6

Explanation:

The position of an object at time t is given by s(t) = -2 - 6t

To find instantaneous velocity we take derivative s'(t)

s(t)= -2-6t

s'(t)= 0 -6=-6

To find instantaneous velocity at t= 2, we plug in 2 for t

there is no 't' in s'(t)

so s'(2)= -6

the instantaneous velocity at t = 2 is -6