Sure, let's work through this problem step-by-step.
We start with the equation of motion given by:
[tex]\[ s = ut + \frac{1}{2} a t^2 \][/tex]
Next, we need to substitute the given values into this equation. The values provided are:
[tex]\[ u = 10 \][/tex]
[tex]\[ a = -2 \][/tex]
[tex]\[ t = \frac{1}{2} \][/tex]
### Step 1: Compute [tex]\( ut \)[/tex]
First, let's compute the term involving initial velocity and time ([tex]\( ut \)[/tex]):
[tex]\[ ut = 10 \times \frac{1}{2} \][/tex]
[tex]\[ ut = 10 \times 0.5 \][/tex]
[tex]\[ ut = 5.0 \][/tex]
### Step 2: Compute [tex]\(\frac{1}{2} a t^2\)[/tex]
Next, let's compute the term involving acceleration and time squared [tex]\(\left(\frac{1}{2} a t^2\right)\)[/tex]:
[tex]\[ \frac{1}{2} a t^2 = \frac{1}{2} \times (-2) \times \left(\frac{1}{2}\right)^2 \][/tex]
[tex]\[ \frac{1}{2} a t^2 = \frac{1}{2} \times (-2) \times \frac{1}{4} \][/tex]
[tex]\[ \frac{1}{2} a t^2 = -1 \times \frac{1}{4} \][/tex]
[tex]\[ \frac{1}{2} a t^2 = -0.25 \][/tex]
### Step 3: Sum the terms to find [tex]\( s \)[/tex]
Now, we add the two computed terms to find [tex]\( s \)[/tex]:
[tex]\[ s = ut + \frac{1}{2} a t^2 \][/tex]
[tex]\[ s = 5.0 + (-0.25) \][/tex]
[tex]\[ s = 5.0 - 0.25 \][/tex]
[tex]\[ s = 4.75 \][/tex]
So, the value of [tex]\( s \)[/tex] is [tex]\( 4.75 \)[/tex].
