For this problem, we're asked to find the **acceleration** and **distance traveled** by a car given its **initial velocity**, **final velocity**, and the **time it takes** to change speeds.

When solving problems with uniformly accelerated motion (UAM), Step Zero is **making sure that the acceleration is constant**—*otherwise our kinematics equations don’t apply*. Then we'll follow these steps to solve the problem:

- Identify the
,__target__and unknown variables for each part of the problem—remember that__known__*only*(Δ**3**of the**5**variables*x*,*v*_{0},*v*,_{f}*a*, and*t*)*are needed*to solve any kinematics problem. __Choose a UAM equation__with**only one unknown**, which should be our**target variable**.__Solve the equation__for the target variable, then__substitute__**known values**and__calculate__the answer.

The four UAM (kinematics) equations are:

$\overline{)\mathbf{}{{\mathit{v}}}_{{\mathit{f}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathbf{}}{\mathbf{+}}{\mathit{a}}{\mathit{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathit{x}}{\mathbf{=}}{\mathbf{}}\mathbf{\left(}\frac{{\mathbf{v}}_{\mathbf{f}}\mathbf{+}{\mathbf{v}}_{\mathbf{0}}}{\mathbf{2}}\mathbf{\right)}{\mathit{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathit{x}}{\mathbf{=}}{\mathbf{}}{{\mathit{v}}}_{{\mathbf{0}}}{\mathit{t}}{\mathbf{+}}{\frac{1}{2}}{\mathit{a}}{{\mathit{t}}}^{{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}{\mathbf{}}{{{\mathit{v}}}_{{\mathit{f}}}}^{{\mathbf{2}}}{\mathbf{=}}{\mathbf{}}{{{\mathit{v}}}_{{\mathbf{0}}}}^{{\mathbf{2}}}{\mathbf{}}{\mathbf{+}}{\mathbf{2}}{\mathit{a}}{\mathbf{\u2206}}{\mathit{x}}}$

A car accelerates from 13 m/s to 23 m/s in 6.5 s.**(a)** What was its acceleration? Assume constant acceleration.**(b)** How far did it travel in this time? Assume constant acceleration.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Kinematics Equations concept. You can view video lessons to learn Kinematics Equations. Or if you need more Kinematics Equations practice, you can also practice Kinematics Equations practice problems.