Question

Автомобиль движется по арочному мосту с радиусом 100 метров по уравнению S=10t+t во второй степени Определить полное ускорение автомобиля через 3 секунды

Answer 1

V=10+2*t
Тангенциальное ускорение ат=2 м/с²
ан=v²/R=(10+2*t)²/R=(10+2*3)²/100=2.56 м/с²
Полное ускорение
a=√(ат²+ан²)=√(2²+2,56²)=3,25 м/с²
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Answer 2

Calculation of the Total Acceleration of the Car

To determine the total acceleration of the car, we need to find the second derivative of the equation for displacement with respect to time. The given equation for displacement is:

S = 10t + t^2

Taking the derivative of this equation with respect to time, we get the equation for velocity:

v = dS/dt = 10 + 2t Taking the derivative of the velocity equation with respect to time, we get the equation for acceleration:

a = dv/dt = 2 Therefore, the total acceleration of the car is a constant value of 2 m/s^2.

Calculation of the Centripetal Acceleration of the Car

Since the car is moving on an arched bridge with a radius of 100 meters, we can calculate the centripetal acceleration using the formula:

a_c = v^2 / r

Substituting the given values, we have:

a_c = (10 + 2t)^2 / 100

To find the centripetal acceleration after 3 seconds, we substitute t = 3 into the equation:

a_c = (10 + 2(3))^2 / 100 = (10 + 6)^2 / 100 = 16^2 / 100 = 256 / 100 = 2.56 m/s^2

Therefore, the centripetal acceleration of the car after 3 seconds is 2.56 m/s^2.

Conclusion

The total acceleration of the car is a constant value of 2 m/s^2, while the centripetal acceleration of the car after 3 seconds is 2.56 m/s^2.