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?

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:

Step-by-step explanation:

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

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

And if we take the derivate we got:

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:

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."