Question

Suppose the position of an object moving in a straight line is given by s (t )equals 4 t2+ 5 t+ 5. Find the instantaneous velocity when t equals 2. What expression can be used to find the instantaneous velocity at the given​ time?

Answer 1

Answer:

$v(t) = 8t +5$

And that represent the instantaneous velocity at a given time t.

And then we just need to replace t =2 in order to find the instantaneous velocity and we got:

$v(t=2) = 8*2 + 5 = 16+5 = 21$

Step-by-step explanation:

For this case we have the position function s(t) given by:

$s(t) = 4t^2 + 5t+5$

And we can calculate the instanteneous velocity with the first derivate respect to the time, like this:

$v(t) = s'(t)= \frac{ds}{dt}$

And if we take the derivate we got:

$v(t) = 8t +5$

And that represent the instantaneous velocity at a given time t.

And then we just need to replace t =2 in order to find the instantaneous velocity and we got:

$v(t=2) = 8*2 + 5 = 16+5 = 21$