Question

What is the velocity of an object accelerating at 7.0 m/s² after 4.0s when it is initially moving at 3.0 m/s? Value​

Answer 1

31.0 m/s

Step-by-step explanation:

Given:

`\vec a=7.0 \ m/s^2\\\\t=4.0 \ s\\\\\vec v_0 = 3.0 \ m/s`

Find:
`\vec v_f=?? \ m/s`

`\boxed{\left\begin{array}{ccc}\text{\underline{The 4 Kinematic Equations:}}\\\\1. \ \vec v_f=\vec v_0+\vec at\\\\2. \ \Delta \vec x=(1)/(2)(\vec v_f-\vec v_0)t\\\\3. \ \Delta \vec x=\vec v_0t+(1)/(2)\vec at^2\\\\ 4. \ \vec v_f^2=\vec v_0^2+2\vec a \Delta \vec x \end{array}\right}`

Using the first kinematic equation:

`\vec v_f=\vec v_0+\vec at\\\\\Longrightarrow \vec v_f=3.0+(7.0)(4.0)\\\\\Longrightarrow \vec v_f=3.0+28.0\\\\\therefore \boxed{\boxed{\vec v_f=31.0 \ m/s}}`

Thus, the objects final velocity is found.