For this problem, we're asked to find the **time** taken by an accelerating object to reach target speed.

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:

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

The head of a rattlesnake can accelerate at 50m/s^{2} in striking a victim. If a car could do as well, how long would it take to reach a speed of 100km/h from rest?