Question

Движение материальной точки задано уравнением x=4t-0,05t2 . Определить момент времени, в который скорость точки равна нулю. Найти координаты и ускорение в этот момент.

Answer 1

V(t)=x'(t)=4-0.1t
0=4-0.1t
t=40c
x(40)=4*40-0.05*100*16=160-5*16=160-80=80 -координата -она же пройденный путь-80м
a(t)=V'(t)=-0.1
т.е. ускорение не зависит от времени и является отрицательным - значит перед нами равнозамедленное движение.

Answer 2

Equation of Motion and Finding the Time when Velocity is Zero

The equation of motion for the given problem is given by:

x = 4t - 0.05t^2

To find the moment in time when the velocity of the particle is zero, we need to find the time when the derivative of the position function with respect to time is zero. The derivative of the position function gives us the velocity function.

Let's find the derivative of the position function:

v = dx/dt = d(4t - 0.05t^2)/dt

Differentiating the equation with respect to time, we get:

v = 4 - 0.1t

Now, we need to find the time when the velocity is zero. Setting the velocity function equal to zero, we can solve for t:

0 = 4 - 0.1t

Solving this equation, we find:

t = 40

Therefore, at t = 40, the velocity of the particle is zero.

Coordinates and Acceleration at the Moment when Velocity is Zero

To find the coordinates and acceleration at the moment when the velocity is zero, we need to substitute the value of t = 40 into the position function and the acceleration function.

Let's find the coordinates at t = 40:

x = 4t - 0.05t^2

Substituting t = 40 into the equation, we get:

x = 4(40) - 0.05(40)^2

Simplifying the equation, we find:

x = 160 - 0.05(1600)

x = 160 - 80

x = 80

Therefore, at t = 40, the x-coordinate of the particle is 80.

To find the y-coordinate, we need more information about the problem. If the problem provides the y-coordinate equation or any other information, please provide it so that we can calculate the y-coordinate.

Now, let's find the acceleration at t = 40:

a = dv/dt = d(4 - 0.1t)/dt

Differentiating the equation with respect to time, we get:

a = -0.1

Therefore, at t = 40, the acceleration of the particle is -0.1.

To summarize: - At t = 40, the velocity of the particle is zero. - At t = 40, the x-coordinate of the particle is 80. - At t = 40, the acceleration of the particle is -0.1.