Question

Зависимость пути от времени при прямолинейном движении двух тел задана уравнениями s1=2/3t(в кубе)+t(в квадрате)-t+14 ; s2=2/3t(в кубе)-1/2t(в квадрате)+11t-8 в какой момент времени их скорости будут равны

Answer 1

S1'=2t²+2t-1   s2'=2t²-t+11   v=s'
2t²+2t-1=2t²-t+11
3t=12   t=4  скорости сравняются через t=4

Answer 2

Calculating the Time When Their Velocities Are Equal

To find the time when the velocities of the two bodies are equal, we can start by differentiating the given equations for displacement with respect to time to obtain the equations for velocity. Then, we can set these two velocity equations equal to each other and solve for the time when their velocities are equal.

The given equations for displacement are: - s1 = (2/3)t^3 + t^2 - t + 14 - s2 = (2/3)t^3 - (1/2)t^2 + 11t - 8

Differentiating the Displacement Equations to Obtain Velocity Equations

Let's differentiate the displacement equations to obtain the velocity equations.

The derivative of s1 with respect to t gives the velocity v1: - v1 = ds1/dt = 2t^2 + 2t - 1

The derivative of s2 with respect to t gives the velocity v2: - v2 = ds2/dt = 2t^2 - t + 11

Setting the Velocity Equations Equal to Each Other

Now, we can set v1 equal to v2 and solve for the time when their velocities are equal: - 2t^2 + 2t - 1 = 2t^2 - t + 11

Solving for the Time When Their Velocities Are Equal

By solving the equation 2t^2 + 2t - 1 = 2t^2 - t + 11, we can find the time when their velocities are equal.

Let's solve for t: - 2t^2 + 2t - 1 = 2t^2 - t + 11 - 3t = 12 - t = 4

Therefore, their velocities will be equal at t = 4.

This is the time when the velocities of the two bodies will be equal.

(#1)(#2)