Question

for the three - step question that follows, provide your answer to each part in the given workspace. identify each step with a coordinating response. part a: the formula used to find the displacement, s, of an object is s = v_i t+1/2 at^2. rearrange the formula for v_i. part b: the formula used to find the displacement, s, of an object is s = v_i t+1/2 at^2. rearrange the formula for a. part c: show your work for parts a and b to support your answers.

Explanation:

Step1: Rearrange formula for \(v_i\)

Starting with \(s = v_it+\frac{1}{2}at^{2}\), we first isolate the term with \(v_i\). Subtract \(\frac{1}{2}at^{2}\) from both sides:
\[s-\frac{1}{2}at^{2}=v_it\]
Then divide both sides by \(t\) (assuming \(t
eq0\)) to get \(v_i=\frac{s - \frac{1}{2}at^{2}}{t}=\frac{s}{t}-\frac{1}{2}at\)

Step2: Rearrange formula for \(a\)

Starting with \(s = v_it+\frac{1}{2}at^{2}\), we first isolate the term with \(a\). Subtract \(v_it\) from both sides:
\[s - v_it=\frac{1}{2}at^{2}\]
Then multiply both sides by \(2\) to get \(2(s - v_it)=at^{2}\)
Finally, divide both sides by \(t^{2}\) (assuming \(t
eq0\)) to get \(a=\frac{2(s - v_it)}{t^{2}}\)

Answer:

For \(v_i\): \(v_i=\frac{s}{t}-\frac{1}{2}at\)
For \(a\): \(a=\frac{2(s - v_it)}{t^{2}}\)