A car enters a 200 m ramp at 10.0 m/s and accelerates at 2.00 m/s^2. How long does it take to travel the 200 m?

1. Identify the knowns: the initial velocity is 10.0 m/s, the acceleration is 2.00 m/s^2 and the displacement is 200 m. 2. Use displacement equals initial velocity times time plus half the acceleration times time squared. 3. Substitute the values: 200 = 10.0t + 0.5 x 2.00 x t^2, so 200 = 10t + t^2. 4. Rearrange into standard form: t^2 + 10t - 200 = 0. 5. Apply the quadratic formula with a = 1.00, b = 10.0 and c = -200. 6. The two roots are t = 10.0 s and t = -20.0 s. 7. A negative time would place the event before the motion began, so discard it and take 10.0 s. 8. Dividing 200 m by 10.0 m/s gives 20.0 s and ignores the acceleration altogether. _Source: OpenStax College Physics (CC BY 4.0), Ch 2 "Kinematics", section 2.5 Motion Equations for Constant Acceleration in One Dimension_