Solution to problem 7.4.16 from the collection of Kepe O.E.

Problem 7.4.16: The equations of motion of a point are given: x = 0.01 t3, y = 200 - 10t. It is necessary to determine the acceleration of a point at the moment of time when it crosses the Ox axis. (Answer 1,2)

To solve this problem, you need to find the acceleration of the point, that is, the second derivative of its coordinates with respect to time. First, we find the coordinate t0 of the moment of time when the point intersects the Ox axis, i.e. when y = 0: 0.01 t0^3 = 200 - 10t0, from which we obtain t0 = 5. Next, we find the second derivatives of the coordinates x and y: x'' = 0.06t, y'' = -10. At time t0 = 5, the acceleration of the point will be x''(t0) = 0.3, which is the answer to the problem.

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Problem 7.4.16 from the collection of Kepe O.?. consists in determining the acceleration of a point at the moment of time when it crosses the Ox axis, with given equations of motion: x = 0.01 t^3 and y = 200 - 10t.

To solve the problem, it is necessary to find the moment of time t when the point intersects the Ox axis. To do this, you need to solve the equation 0.01 t^3 = 0, which gives t = 0.

Then you need to find the value of the speed of the point at time t = 0, using the derivative of the equation of motion with respect to time:

dx/dt = 0,03 t^2

dy/dt = -10

At t = 0 we obtain the speed of the point along the Ox axis:

v = dx/dt = 0

And acceleration is defined as the derivative of speed with respect to time:

a = dv/dt = d/dt (dx/dt) = 0,06 t

At t = 0, we obtain the acceleration of the point at the moment of crossing the Ox axis:

a = 0,06 * 0 = 0

Thus, the answer to problem 7.4.16 from the collection of Kepe O.?. is 0.

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