Question

Точка движется по координатной прямой согласно закону x t =0.5t 2-3t=5.где x(t) координата точки в момент времени t. в како момент времени скорость точки будет равна 9?

Answer 1

Примерно так:
v(t) = x' (t) = (0,5t² - 3t + 5)' = t - 3.
По условию v(t) = 9, тогда t - 3 = 9, отсюда t = 12.
Ответ: 12 

Answer 2

Problem Analysis

The problem provides a law of motion for a point moving along a coordinate axis: \(x(t) = 0.5t^2 - 3t + 5\), where \(x(t)\) is the coordinate of the point at time \(t\). We need to find the time at which the velocity of the point will be equal to 9.

Solution

To find the time at which the velocity of the point will be equal to 9, we need to differentiate the position function \(x(t)\) to obtain the velocity function \(v(t)\), and then solve for the time when the velocity is 9.

The velocity function \(v(t)\) is the derivative of the position function \(x(t)\) with respect to time \(t\). Therefore, we have:

\[v(t) = \frac{dx}{dt}\]

Calculating Velocity

Differentiating the position function \(x(t) = 0.5t^2 - 3t + 5\) with respect to time \(t\) gives us the velocity function \(v(t)\).

\[v(t) = \frac{dx}{dt} = t - 3\]

Finding the Time

To find the time at which the velocity of the point will be equal to 9, we set the velocity function \(v(t)\) equal to 9 and solve for \(t\):

\[t - 3 = 9\]

Solving for \(t\):

\[t = 9 + 3\]

\[t = 12\]

Therefore, the velocity of the point will be equal to 9 at time \(t = 12\).

Final Answer

The velocity of the point will be equal to 9 at time \(t = 12\).