Bad drivers

Classical Mechanics Level 2

You are driving a car at \(30\text{ m/s}\) when a bad driver traveling at a constant speed of \(20\text{ m/s}\) swerves into your lane \(20\) meters ahead. As soon as you see the car in front of you, you begin to brake. What is the smallest deceleration needed, in \(\text{m/s}^2,\) to avoid rear-ending the car? You may assume your acceleration is constant.