This problem starts with a vehicle traveling at some constant vel-ocity and the driver noticing an obstacle or danger ahead. There's a time period *after the driver notices the problem* where the vehicle **continues with a constant velocity**, then the driver brakes and the vehicle has a **constant deceleration**. Whenever we have a problem like this, we'll follow these steps:

__Break the problem into__. We'll label the two ends of each interval with letters (A, B, C...) It can also help to draw a diagram, as you might have seen in some of our videos!**different intervals**- Identify the
for the problem.**target variable** - Identify the
__known variables____for__.__each interval__ __Choose the UAM equations__that relate the known variables to the target variable.- Solve for the target.

The four UAM (kinematics) equations are:

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

For problems that involve a reaction time and stopping distance, we'll always have **two intervals** for **Step 1**, as shown below:

We'll also use a **standard coordinate system** where the +*x*-axis points __in the direction of travel__. That means __ a is negative__, since the acceleration is in the opposite direction (slowing down).

An inattentive driver is traveling 18.0 m/s when he notices a red light ahead. His car is capable of decelerating at a rate of 3.61 m/s^{2} .

If it takes him 0.210 s to get the brakes on and he is 67.0 m from the intersection when he sees the light, will he be able to stop in time?

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.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Jerousek's class at UCF.