Solution to problem 14.3.5 from the collection of Kepe O.E.

14.3.5 A material point with mass m = 4 kg is acted upon by a force F = 4i + tj.

It is necessary to find the projection of the speed of the point onto the Oy axis at the time t = 2 s, if the movement begins from a state of rest.

Answer: 0.5.

From the conditions of the problem we know the mass of the material point m = 4 kg and the force acting on it F = 4i + tj. The movement begins from a state of rest, which means the initial speed of the point is zero. It is necessary to find the projection of the point’s velocity onto the Oy axis at time t = 2 s.

To solve the problem, you can use the formula for calculating speed at constant acceleration: v = u + at,

where v is the final speed, u is the initial speed, a is acceleration, t is time.

The acceleration of a point can be determined using Newton's second law: F = at,

where F is the force acting on the point, m is its mass, and a is the acceleration.

We can decompose the force into projections of axes Ох and Оу: F_x = 4, F_y = t.

Thus, the acceleration of the point will be equal to: a_y = F_y / m = t / m.

Since the initial speed is zero, the speed of the point at time t will be equal to the product of acceleration and time: v_y = a_y * t = t / m * t = t^2 / m.

Substituting the values, we get: v_y = 2^2 / 4 = 0.5.

Thus, the projection of the point’s velocity onto the Oy axis at time t = 2 s is equal to 0.5.

Solution to problem 14.3.5 from the collection of Kepe O.?.

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A digital product is presented - a solution to problem 14.3.5 from the collection of Kepe O.?. This product is intended for those who are looking for an effective way to prepare for exams or want to improve their knowledge in the field of physics.

In the problem it is known that a force F = 4i + tj acts on a material point with a mass of 4 kg, and the initial velocity of the point is zero. It is necessary to find the projection of the point’s velocity onto the Oy axis at time t = 2 s.

To solve the problem, a formula is used to calculate speed at constant acceleration: v = u + at, where v is the final speed, u is the initial speed, a is acceleration, t is time.

The acceleration of a point is determined by Newton's second law: F = ma, where F is the force acting on the point, m is its mass, a is acceleration.

Next, the force is decomposed into projections on the Ox and Oy axes: F_x = 4, F_y = t. Thus, the acceleration of the point will be equal to: a_y = F_y / m = t / m.

Since the initial speed is zero, the speed of the point at time t will be equal to the product of acceleration and time: v_y = a_y * t = t / m * t = t^2 / m. Substituting the values, we get: v_y = 2^2 / 4 = 0.5.

Thus, the projection of the point’s velocity onto the Oy axis at time t = 2 s is equal to 0.5.

By purchasing this digital product, you will receive a detailed and understandable solution to the problem, which was completed by qualified specialists in the field of physics. The solution will be designed in accordance with the requirements of modern design, which will allow you to comfortably use it on any device.

Also, this product will give you the opportunity to quickly and effectively prepare for exams or improve your knowledge in the field of physics. Don't miss the opportunity to purchase our digital product and improve your physics knowledge today!

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Solution to problem 14.3.5 from the collection of Kepe O.?. consists in determining the projection onto the Oy axis of the velocity of a material point with a mass of 4 kg at the time t = 2 s, if initially the point was at rest and was acted upon by a force F = 4i + tj.

To solve the problem it is necessary to use the equations of motion. Since the material point was at rest, its initial velocity is zero. Taking this into account, we can write the following equation for the projection of velocity onto the Oy axis:

v_y = ∫a_y dt

where a_y is the projection of the acceleration of the point onto the Oy axis.

To find the acceleration projection, you need to use Newton's second law:

F = ma

where F is the force acting on a material point, m is its mass, and a is acceleration.

Expanding the force F into projections on the Ox and Oy axes, we obtain:

F_x = 4 F_y = t

The acceleration projection onto the Oy axis is equal to:

a_y = F_y / m = t / m

Now you can substitute the value of the acceleration projection into the equation for the velocity projection and integrate:

v_y = ∫a_y dt = ∫(t / m) dt = (1/2) * (t^2 / m)

At t = 2 s and m = 4 kg we obtain:

v_y = (1/2) * ((2 s)^2 / 4 kg) = 0.5 m/c

Thus, the projection of velocity onto the Oy axis at time t = 2 s is equal to 0.5 m/s.

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