Solution to problem 7.4.19 from the collection of Kepe O.E.

7.4.19

Given: the point moves rectilinearly with acceleration a = 0.2 t. Initial speed v₀ = 0 at time t₀ = 0.

Find: the moment of time t at which the speed of the point will be equal to 2 m/s.

Answer:

From the equation of motion with constant acceleration:

v = v₀ + at

where v is the speed at time t, v₀ - initial speed, a - acceleration.

Substituting the data from the problem statement, we get:

2 = 0 + 0,2t

t = 2 / 0,2 = 10

Answer: t = 10 s.

Let's reformulate the problem:

Given the acceleration of a point moving rectilinearly and the initial speed at time t₀. It is necessary to find the moment of time t when the speed of the point becomes equal to 2 m/s.

The solution to the problem is based on the equation of motion with constant acceleration, where the speed of a point at time t is expressed through the initial speed, acceleration and time:

v = v₀ + at

Substituting known values, we get:

2 = 0 + 0,2t

Where can we find the time value:

t = 2 / 0,2 = 10

Thus, the moment of time t, when the speed of the point is equal to 2 m/s, is equal to 10 s.

Solution to problem 7.4.19 from the collection of Kepe O..

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Solution to problem 7.4.19 from the collection of Kepe O.?. consists in determining the moment of time t when the speed of a point moving rectilinearly with acceleration a = 0.2 t will be equal to 2 m/s. Initial data of the problem: at t0 = 0, speed v0 = 0.

To solve the problem, you need to use the equation of motion: v = v0 + at, where v is the speed at time t, v0 is the initial speed, and is the acceleration.

Integrating this equation, we obtain the path equation: x = x0 + v0t + (1/2)at^2, where x is the displacement at time t, x0 is the initial position.

From the conditions of the problem it is known that the speed of the point should be equal to 2 m/s. Substituting this value into the equation of motion and solving the equation for t, we obtain the moment of time t when this condition is met.

So, substituting the known values, we get:

2 = 0 + 0.2t t = 10 seconds

Now, knowing the time t, we can find the displacement of the point during this time using the path equation:

x = x0 + v0t + (1/2)at^2 x = 0 + 0 + (1/2) * 0,2 * (10)^2 x = 10 м

The answer to the problem is time t, equal to 4.47 seconds (rounded to two decimal places).

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