It is known that there is a relationship between the braking distance S (unit: meter) and the vehicle speed V (unit: meter/second): s=tv+kv2, where T is the driver's reaction time (unit: second) and K is the braking coefficient. In order to test the change of braking distance of drivers after drinking, a certain institution conducted a "drunk" driving test on a certain type of car, and it was known that the braking coefficient of this type of car was k = 0.66.
(1) If volunteers don't drink and the speed is 10 m/s, the braking distance of the car is 15.
15
Rice;
(2) After drinking a bottle of beer for half an hour, the volunteers drove at the speed of 15m/s, and the braking distance was 52.5m At this time, the response time of the volunteers was 2.
2
second
(3) If volunteers drive at the speed of 10 m/s, how much will the braking distance increase compared with those who don't drink?
(4) If you drive this type of car at a speed of 10 m/s to 15 m/s in the future, and the distance between you and the vehicle in front is kept between 42 m and 50 m, if you find that the vehicle in front stops suddenly, how many seconds should your reaction time be to prevent "rear-end"? Test center: the application of linear function. Special topic: Travel problem. Analysis: (1) substitute k=0. 1, t=0.5, v= 10 to get the braking distance;
(2) Substitute k=0. 1, v= 15 and s=20 into a given function to get the value of t;
(3) Substitute k=0. 1, v= 10 and t=2 into the given function to get the braking distance, and compare it with (1);
(4) Substitute k=0. 1, v= 15 and s=42 into the given function to get the value of t. Solution: (1) When k=0. 1, t=0.5 and v = 65433.
s = 0.5× 10+0. 1× 102 = 15m。
So the answer is:15;
(2)52.5 = 15t+0. 1× 152
The solution is t = 2.
So the answer is 2;
(3) When t=2 and v= 10, S = 2×10+0./kloc-0 /×102 = 30 (m).
30- 15= 15 (m).
Answer: The braking distance will be increased by15m compared with that without drinking;
(4) When v= 15 and s=42,
42 = 15t+0. 1× 152
t= 1.3。
Therefore, the reaction time should not exceed 1.3 seconds.