Question

При движении тела по прямой расстояние S( в метрах) до точки отсчёта изменялось по закону: S(t)= 5t^2+6t, где t- время в секундах, прошедшее от начала дыижения. Вычислите скорость тела (в м/c) через 7 секунд после начала движения?

Answer 1

Эта задача больше по физике
есть общая формула
S=vot+at^2/2
отсюда vo=6, a=10
тогда v можно найти из формулы ускорения
v=vo+at=6+10*7=76м/с
ответ:76м/с

Answer 2

Calculating the Velocity of an Object

To calculate the velocity of the object at a specific time, we can use the formula for velocity, which is the derivative of the position function with respect to time.

The position function given is: S(t) = 5t^2 + 6t

To find the velocity at a specific time, we need to find the derivative of the position function with respect to time.

The derivative of the position function with respect to time is the velocity function, which can be found using the power rule of differentiation.

The power rule states that if we have a function of the form f(x) = ax^n, then the derivative is f'(x) = n * ax^(n-1).

Calculating the Derivative

The position function is S(t) = 5t^2 + 6t. To find the velocity function, we need to find the derivative of S(t) with respect to t.

The derivative of S(t) with respect to t is: S'(t) = d(S(t))/dt = 10t + 6

Calculating the Velocity at t = 7 seconds

Now, to find the velocity at t = 7 seconds, we can substitute t = 7 into the velocity function S'(t) = 10t + 6.

Substituting t = 7 into the velocity function gives us: S'(7) = 10(7) + 6 = 70 + 6 = 76 m/s

Therefore, the velocity of the object at t = 7 seconds is 76 m/s.