V(t) = 5-2/3t S = Vot-at/2; Vo-?

To find the initial velocity (\(V_0\)) from the given equation for velocity \(V(t) = 5 - \frac{2}{3}t\), we need to evaluate \(V(t)\) at time \(t = 0\).

Step 1: Calculate \(V(0)\)

\[ V(0) = 5 - \frac{2}{3}(0) = 5 \]

So, the initial velocity \(V_0 = V(0) = 5\) m/s.

Step 2: Understanding the equation for displacement

The equation for displacement \(S\) given is:

\[ S = V_0 t - \frac{a t^2}{2} \]

Here, \(V_0\) is the initial velocity, \(a\) is acceleration, and \(t\) is the time.

Step 3: Finding acceleration (\(a\))

From the velocity equation \(V(t) = 5 - \frac{2}{3}t\), we can find the acceleration by determining the slope (the coefficient of \(t\)):

\[ a = -\frac{2}{3} \]

Step 4: Summary of results

So, we have:

• Initial velocity \(V_0 = 5 \text{ m/s}\)
• Acceleration \(a = -\frac{2}{3} \text{ m/s}^2\)

Now, you can use these values in the displacement equation if needed. If you have any specific questions or need further assistance, feel free to ask!