Question

Машину ГАИ, движущуюся с постоянной скоростью 80 км/ч, обогнал лихач имевший скорость 160 км/ч.Ровно через 1 с инспектор нажал на акселератор. Если ускорение автомобиля ГАИ равно 3м/с, то сколько времени понадобится, чтобы догнать лихача,считая что он движется с постоянной скоростью Р.S. ответ должен получиться 15,74 сек

Answer 1

V01=80 км/ч = 80/3,6 м/с =22,22 м/с - ---- начальная скорость ГАИ 

V2=160 км/ч = 160/3,6 м/с   = 44,44 м/с ------  скорость лихача постоянная

t+1 ---- двигался лихач, после обгона ГАИ пока его не догнали 

t ----  двигался инспектор пока не догнал лихача

 чтобы ГАИ догнал лихача, должно выполняться S1=S2,

где S1 и S2   ----  путь который преодолел ГАИ и лихач соответственно

S1=V01*t+a*t*t/2

S2=V2*(t+1)

V01*t+a*t*t/2=V2*(t+1)

 

22,22*t+3*t*t/2=44,44*t+44,44

1,5*t*t - 22,22*t - 44,44=0

D=493,7284+266,64=760,3684

t=(22,22+27,57)/3=16,6

 

Ответ t=16,6 сек (проверял по моему решению твой ответ не подходит)

 

Answer 2

Problem Analysis

To solve this problem, we need to calculate the time it takes for the car traveling at a constant speed of 80 km/h to catch up with the reckless driver traveling at a constant speed of 160 km/h. Additionally, we are given that the acceleration of the police car is 3 m/s².

Solution

First, let's calculate the distance the reckless driver travels in 1 second at a speed of 160 km/h. Then, we'll calculate the distance the police car travels in 1 second at a speed of 80 km/h and with an acceleration of 3 m/s². Finally, we'll determine the time it takes for the police car to catch up with the reckless driver.

1. Calculate the distance the reckless driver travels in 1 second at a speed of 160 km/h: - Convert the speed from km/h to m/s: - 160 km/h = (160 * 1000 m) / (3600 s) = 44.44 m/s - Distance traveled in 1 second = speed * time = 44.44 m/s * 1 s = 44.44 m

2. Calculate the distance the police car travels in 1 second at a speed of 80 km/h and with an acceleration of 3 m/s²: - Convert the speed from km/h to m/s: - 80 km/h = (80 * 1000 m) / (3600 s) = 22.22 m/s - Distance traveled in 1 second at constant speed = speed * time = 22.22 m/s * 1 s = 22.22 m - Calculate the additional distance covered due to acceleration using the equation: - Distance = initial velocity * time + 0.5 * acceleration * time^2 - Distance = 22.22 m + 0.5 * 3 m/s² * (1 s)^2 = 22.22 m + 1.5 m = 23.72 m

3. Determine the time it takes for the police car to catch up with the reckless driver: - Time = Distance traveled by the reckless driver / (Distance traveled by the police car - Additional distance covered due to acceleration) - Time = 44.44 m / (23.72 m - 22.22 m) = 44.44 m / 1.5 m = 29.63 s

Conclusion

The time it takes for the police car to catch up with the reckless driver is approximately 29.63 seconds. This result does not match the provided answer of 15.74 seconds. If there are any additional details or constraints that need to be considered, please provide them for further analysis.