When calculating \( x = vt + \frac{1}{2}at^2 \), what is the value of \( x \) if \( v = 0.227 \, m/s \), \( t = 11.1 \, s \), and \( a = 9.80 \, m/s^2 \)?

To find the value of ( x ) using the equation ( x = vt + \frac{1}{2}at^2 ), you can substitute the given values into the equation.

First, substitute the values:

• ( v = 0.227 , m/s )

• ( t = 11.1 , s )

• ( a = 9.80 , m/s^2 )

Calculate the first term ( vt ):

[

vt = 0.227 , m/s \times 11.1 , s = 2.52 , m

]

Next, calculate the term ( \frac{1}{2}at^2 ):

[

\frac{1}{2}at^2 = \frac{1}{2} \times 9.80 , m/s^2 \times (11.1 , s)^2

]

First, calculate ( (11.1 , s)^2 ):

[

(11.1 , s)^2 = 123.21 , s^2

]

Now denote ( \frac{1}{2} \times 9.80 ):

\