example 6 - 1 dim motion\na car is traveling at 20.0 m/s, and the driver sees a traffic light turn red…

example 6 - 1 dim motion\na car is traveling at 20.0 m/s, and the driver sees a traffic light turn red. after 0.530 s (the reaction time), the driver applies the brakes, and the car decelerates at 7.00 m/s². what is the stopping distance of the car, as measured from the point where the driver first sees the red light? 10.6 m + 28.6 m = 39.2 m

example 6 - 1 dim motion\na car is traveling at 20.0 m/s, and the driver sees a traffic light turn red. after 0.530 s (the reaction time), the driver applies the brakes, and the car decelerates at 7.00 m/s². what is the stopping distance of the car, as measured from the point where the driver first sees the red light? 10.6 m + 28.6 m = 39.2 m

Answer

Explanation:

Step1: 反应时间内行驶距离

$d_1 = v_0 \times t_{\text{react}} = 20.0 , \text{m/s} \times 0.530 , \text{s} = 10.6 , \text{m}$

Step2: 刹车距离计算

由$v^2 = v_0^2 + 2ad_2$，$v=0$得$d_2 = \frac{0 - v_0^2}{2a} = \frac{-20.0^2}{2 \times (-7.00)} \approx 28.6 , \text{m}$

Step3: 总停车距离

$d = d_1 + d_2 = 10.6 , \text{m} + 28.6 , \text{m} = 39.2 , \text{m}$

Answer:

39.2 m