Suppose that an object is moving along the ground and that the distance (in centimeters) it has travelled after t seconds is given by the formula f(t)=t2 cm. calculate the average speed during the 1 millionth of a second after t=3.

The average speed is the average rate of change of the function.

The average speed during the 1 millionth of a second after t=3 is 6 cm/s

The function is given as:

The average rate of a function is:

1 millionth of a second after t=3 means that:

So, we have:

Expand the numerator

Hence, the average speed during the 1 millionth of a second after t=3 is 6 cm/s

Read more about average speed at:

link

It must have the same slope as the given line, so

m = -A/B = -1/-2 = 1/2

So far, we have

y = mx + b = x/2 + b

Use the given point to find b.

4 = -2/2 + b = -1 + b

b = 5

y = x/2 + 5

Multiply through by 2.

2y = x + 10

Standard form:

x - 2y = -10