Solution to problem 14.2.2 from the collection of Kepe O.E.

Let's consider the problem of finding the modulus of the impulse of a force constant in direction, which varies according to the law F = 5 + 9t^2. To find the modulus of the force impulse, it is necessary to integrate the expression for the instantaneous force impulse over time in the interval from t1 to t2:

Substituting the expression for the force F(t), we obtain:

Integrating this expression, we get:

Substituting the values ​​t1 = 0 and t2 = 2 s, we get:

Thus, the modulus of the force impulse over the time interval t = t2 - t1, where t2 = 2 s, t1 = 0, is equal to 34.

Solution to problem 14.2.2 from the collection of Kepe O..

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Problem 14.2.2 from the collection of Kepe O.?. describes the change in the modulus of a constant force in the direction according to the law F = 5 + 9t^2. It is necessary to find the modulus of the impulse of this force over the time interval t = t2 - t1, where t2 = 2 s, t1 = 0.

To solve this problem, it is necessary to find an antiderivative of the function F(t), that is, a function G(t), such that G'(t) = F(t). After this, using the momentum formula, it is necessary to calculate the difference in the values ​​of the function G(t) at points t2 and t1, that is, G(t2) - G(t1), which will give the desired momentum modulus.

Find the antiderivative of the function F(t):

G(t) = ∫(5 + 9t^2)dt = 5t + 3t^3

We calculate the value of the impulse modulus:

|p| = |G(t2) - G(t1)| = |(5t2 + 3t2^3) - (5t1 + 3t1^3)| = |(52 + 32^3) - (50 + 30^3)| = |34| = 34

Answer: the modulus of the impulse of this force over the period of time t = t2 - t1, where t2 = 2 s, t1 = 0, is 34.

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