Question

Два тела начали движение из одной точки в противоположных направлениях,первое тело движется со скоростью v1=2t^2+4t м/с,второе со скоростью v2=3t+2 м/с.На каком расстоянии друг от друга эти тела окажутся через 10 сек.мегахэлп!!

Answer 1

S=s₁+s₂
$s_{1} = \int\limits^a_b { v_{1}(t) } \, dt$
a=10 сек, b= 0 сек
$s_{2} = \int\limits^a_b { v_{2}(t) } \, dt$
$s_{1} = \int\limits ^{10} _0 {(2 t^{2}+4t )} \, dt=(2* \frac{ t^{3} }{3}+2 t^{2} ) | _{0} ^{10} = \frac{2}{3} *1000+200$
$s_{2}= \int\limits ^{10} _0 {(3t+2)} \, dt=(1,5 t^{2} +2t) | _{0} ^{10} =150+20=170$
$s= \frac{2}{3} *1000+200+170=370+ \frac{2000}{3} = \frac{6110}{3}$

ответ: s=6110/3 м

Answer 2

Calculation of Distance between Two Bodies

To find the distance between two bodies that start moving from the same point in opposite directions, we need to integrate their respective velocities over the given time interval.

The velocity of the first body, denoted as v1, is given by the equation v1 = 2t^2 + 4t m/s, where t is the time in seconds.

The velocity of the second body, denoted as v2, is given by the equation v2 = 3t + 2 m/s.

We want to find the distance between the two bodies after 10 seconds.

To calculate the distance, we need to integrate the velocities of both bodies over the given time interval and then find the absolute difference between the two integrated values.

Let's calculate the distance step by step:

1. Integrate the velocity of the first body, v1, over the time interval [0, 10]: - ∫(2t^2 + 4t) dt = [(2/3)t^3 + 2t^2] evaluated from 0 to 10 - [(2/3)(10)^3 + 2(10)^2] - [(2/3)(0)^3 + 2(0)^2] - (2000/3 + 200) - 0 - 2000/3 + 200 - 2600/3 m

2. Integrate the velocity of the second body, v2, over the time interval [0, 10]: - ∫(3t + 2) dt = [(3/2)t^2 + 2t] evaluated from 0 to 10 - [(3/2)(10)^2 + 2(10)] - [(3/2)(0)^2 + 2(0)] - (150/2 + 20) - 0 - 150/2 + 20 - 170 m

3. Find the absolute difference between the integrated values: - |2600/3 - 170| - 2600/3 - 170 - 2600/3 - 510/3 - (2600 - 510)/3 - 2090/3 - Approximately 696.67 meters

Therefore, the two bodies will be approximately 696.67 meters apart after 10 seconds.

Please note that the above calculations are based on the given velocity equations and the assumption that the velocities remain constant over the given time interval.