We are given a function that models the acceleration of a carnival ride.

a = 0.2 v^{2}

In this equation,

a

represents the acceleration towards the center of the ride in meters per second and

v

is the velocity in meters per second. We are asked to graph this function. To help us do that, let's create a table of values for the given function. First, we will fill in the

v

column with any values of

v .

$v$	$0.2 v^{2}$	$a$
$0$
$1$
$1.5$
$2$
$2.5$
$3$

Note that these are only example values of $v$ — we could have chosen any other values and would still get the same graph in the end. Now let's substitute the values of $v$ into the expression $0.2 v^{2} .$

$v$	$0.2 v^{2}$	$a$
$0$	$0.2 (0)^{2}$
$1$	$0.2 (1)^{2}$
$1.5$	$0.2 (1.5)^{2}$
$2$	$0.2 (2)^{2}$
$2.5$	$0.2 (2.5)^{2}$
$3$	$0.2 (3)^{2}$

Next, to find the values of $a,$ we will simplify these expressions.

$v$	$0.2 v^{2}$	$a$
$0$	$0.2 (0)^{2}$	$0$
$1$	$0.2 (1)^{2}$	$0.2$
$1.5$	$0.2 (1.5)^{2}$	$0.45$
$2$	$0.2 (2)^{2}$	$0.8$
$2.5$	$0.2 (6)^{2}$	$1.25$
$3$	$0.2 (3)^{2}$	$1.8$

Let's graph the ordered pairs $(v, a)$ on a coordinate plane!

To finish our graph, we will connect the points with a smooth curve.

Finally, we can estimate the velocity of the ride at an acceleration of $1$ meter per second. Let's draw a horizontal line at $a = 1 .$

Notice that this line crosses our graph at a velocity of about $2.2$

Therefore, at an acceleration of $1$ meter per second, the velocity of the ride is equal to about $2.2$ meters per second.

Exercise