The equation for the motion of a point in a straight line has the form

The equation for the motion of a point in a straight line is written as follows: x = 5 - 2t^3 + t^6 (m).

Need to find:

• path and movement of a point over a period of time from 0 s to 2 s;
• the average speed and average acceleration of the point over this period;
• speed and acceleration of a point at time 2 s.

To solve the problem, let’s find the coordinate values ​​of the point at the initial and final moments of time:

x_beginning = 5 - 2·0^3 + 0^6 = 5 m;

x_con = 5 - 2·2^3 + 2^6 = 69 m.

Path of a point for a given period of time:

S = |x_con - x_beginning| = |69 - 5| = 64 m.

Moving a point over a given period of time:

Δx = x_con - x_beginning = 69 - 5 = 64 m.

Average speed of a point for a given period of time:

V_sr = Δx / Δt = (69 - 5) / 2 = 32,0 м/с.

Average acceleration of a point for a given period of time:

a_sr = V_con - V_beginning / Δt = (0 - 32.0) / 2 = -16.0 m/s².

Speed ​​of the point at time 2 s:

V = dx / dt = -6t^2 + 6t^5 = -24 м/с.

Acceleration of a point at time 2 s:

a = dV / dt = -12t + 30t^4 = 96 м/с2

You are purchasing a unique digital product - a solution to a problem on the topic “Movement of a point in a straight line.”

This product provides a detailed description of the equation of motion of a point in a straight line, which has the form:

x = 5 - 2t^3 + t^6 (м)

The product contains:

• calculation of the path and movement of a point over a period of time from 0 s to 2 s
• determination of the average speed and average acceleration of a point over this period
• calculating the speed and acceleration of a point at a time of 2 s

All information is presented in a beautiful HTML design, which makes the product convenient and easy to read.

By purchasing this digital product, you get not only a solution to the problem, but also a unique experience in studying physics.

You are purchasing a unique digital product - a solution to a problem on the topic “Movement of a point in a straight line.” This product provides a detailed description of the equation of motion of a point in a straight line, which has the form:

x = 5 - 2t^3 + t^6 (м)

The product contains:

• calculation of the path and movement of a point over a period of time from 0 s to 2 s
• determination of the average speed and average acceleration of a point over this period
• calculating the speed and acceleration of a point at a time of 2 s

All information is presented in a beautiful HTML design, which makes the product convenient and easy to read. By purchasing this digital product, you get not only a solution to the problem, but also a unique experience in studying physics.

To solve the problem you need:

1. Find the coordinate values ​​of the point at the initial and final times:

   xstart = 5 - 2·0^3 + 0^6 = 5 m;

   xcon = 5 - 2·2^3 + 2^6 = 69 m.

2. Calculate the path and movement of a point for a given period of time:

   S = |xend - xstart| = |69 - 5| = 64 m.

   Δx = xcon - xnach = 69 - 5 = 64 m.

3. Determine the average speed of a point for a given period of time:

   Vav = Δx / Δt = (69 - 5) / 2 = 32.0 m/s.

4. Calculate the average acceleration of a point for a given period of time:

   asr = Vend - Vstart / Δt = (0 - 32.0) / 2 = -16.0 m/s².

5. Find the speed of the point at time 2 s:

   V = dx / dt = -6t^2 + 6t^5 = -24 м/с.

6. Calculate the acceleration of the point at time 2 s:

   a = dV / dt = -12t + 30t^4 = 96 м/с2

All calculations and conclusions are presented as part of this product. If you have any questions about the solution, don't hesitate to ask. I'll try to help you figure it out.

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