Question

СРОЧНО!!! Тело движется со скоростью Vo. После того, как на него начала действовать постоянная сила в горизонтальном направлении, оно стало двигаться со скоростью x(t)=20t-2,5t2(м). Определитель скорость тела, его координату, путь и перемещение через 10 с после того, как начала действовать сила.

Answer 1

$x(t)=20t-2,5t2(m)\\V_0=20(m/c)\\a=5(m/c^2)\\1)V=V_0+at\\V=20+5*10=20+50=70(m/c)\\2)x(t)=x_0+V_0t+\frac{at^2}{2}\\x(10)=20*10+\frac{5*10}{2}=200+25=225(m)\\3)S=V_0t+\frac{at^2}{2}\\S=20*10+\frac{5*10}{2}=200+25=225(m)$
Перемещение равно тому же, что и S

Answer 2

Problem Statement

A body is moving with an initial velocity of Vo. After a constant force starts acting on it in the horizontal direction, it starts moving with a velocity given by x(t) = 20t - 2.5t^2 (m). Determine the velocity of the body, its coordinate, the distance traveled, and the displacement after 10 seconds from the start of the force.

Solution

To solve this problem, we need to find the velocity, coordinate, distance traveled, and displacement of the body after 10 seconds.

Velocity of the Body

The velocity of the body is given by the function x(t) = 20t - 2.5t^2. To find the velocity at a specific time, we need to take the derivative of x(t) with respect to time (t).

Taking the derivative of x(t) = 20t - 2.5t^2, we get: v(t) = dx(t)/dt = d(20t - 2.5t^2)/dt = 20 - 5t

Therefore, the velocity of the body at any time t is given by v(t) = 20 - 5t.

To find the velocity after 10 seconds, we substitute t = 10 into the equation: v(10) = 20 - 5(10) = 20 - 50 = -30 m/s

The velocity of the body after 10 seconds is -30 m/s.

Coordinate of the Body

The coordinate of the body represents its position along the horizontal axis. In this case, the coordinate is given by the function x(t) = 20t - 2.5t^2.

To find the coordinate at a specific time, we substitute the value of t into the equation. In this case, we need to find the coordinate after 10 seconds: x(10) = 20(10) - 2.5(10)^2 = 200 - 2.5(100) = 200 - 250 = -50 m

The coordinate of the body after 10 seconds is -50 m.

Distance Traveled

The distance traveled by the body represents the total length of the path covered by the body. It is given by the integral of the absolute value of the velocity function over the time interval.

In this case, the velocity function is v(t) = 20 - 5t. To find the distance traveled, we integrate the absolute value of v(t) over the time interval from 0 to 10 seconds:

distance = ∫[0,10] |v(t)| dt = ∫[0,10] |20 - 5t| dt

To evaluate this integral, we need to consider two cases: when 20 - 5t is positive and when it is negative.

Case 1: 20 - 5t > 0 When 20 - 5t > 0, the absolute value of v(t) is equal to v(t). Therefore, the integral becomes: ∫[0,10] (20 - 5t) dt = [20t - (5t^2)/2] from 0 to 10 = (20(10) - (5(10)^2)/2) - (20(0) - (5(0)^2)/2) = (200 - 250) - (0 - 0) = -50 - 0 = -50 m

Case 2: 20 - 5t < 0 When 20 - 5t < 0, the absolute value of v(t) is equal to -(v(t)). Therefore, the integral becomes: ∫[0,10] -(20 - 5t) dt = -∫[0,10] (20 - 5t) dt = -(-50) = 50 m

Since the distance traveled cannot be negative, we take the positive value of 50 m.

The distance traveled by the body after 10 seconds is 50 m.

Displacement

The displacement of the body represents the change in position from the initial position to the final position. It is given by the difference between the coordinates at the initial and final times.

In this case, the initial time is 0 seconds and the final time is 10 seconds. Therefore, the displacement is given by: displacement = x(10) - x(0) = -50 - x(0)

To find x(0), we substitute t = 0 into the equation x(t) = 20t - 2.5t^2: x(0) = 20(0) - 2.5(0)^2 = 0 - 0 = 0

Therefore, the displacement is: displacement = -50 - 0 = -50 m

The displacement of the body after 10 seconds is -50 m.

Summary

After analyzing the given information, we can conclude the following:

- The velocity of the body after 10 seconds is -30 m/s. - The coordinate of the body after 10 seconds is -50 m. - The distance traveled by the body after 10 seconds is 50 m. - The displacement of the body after 10 seconds is -50 m.

Please let me know if you need any further clarification or assistance.