To find the value of [tex]\( v \)[/tex] given the equation [tex]\( v = u + at \)[/tex], and the values [tex]\( u = 2 \)[/tex], [tex]\( a = -5 \)[/tex], and [tex]\( t = \frac{1}{2} \)[/tex], follow these steps:
1. Substitute the given values into the equation:
[tex]\[
v = u + at
\][/tex]
Replacing [tex]\( u \)[/tex] with 2, [tex]\( a \)[/tex] with -5, and [tex]\( t \)[/tex] with [tex]\(\frac{1}{2}\)[/tex], we get:
[tex]\[
v = 2 + (-5) \left( \frac{1}{2} \right)
\][/tex]
2. Calculate the product inside the parentheses:
[tex]\[
-5 \left( \frac{1}{2} \right) = -\frac{5}{2}
\][/tex]
This simplifies to:
[tex]\[
-\frac{5}{2} = -2.5
\][/tex]
3. Add the result to [tex]\( u \)[/tex]:
[tex]\[
v = 2 + (-2.5)
\][/tex]
4. Perform the addition:
[tex]\[
2 + (-2.5) = 2 - 2.5 = -0.5
\][/tex]
Thus, the value of [tex]\( v \)[/tex] is:
[tex]\[
v = -0.5
\][/tex]
