Question

рівняння координати тіла має вигляд x= 10t+2t2. записати рівняння швидкості тіла та побудувати графік залежності прискорення та швидкості від часу​

Answer 1

Ответ:

Дано рівняння залежності координати тіла від часу для рівноприскореного руху, отже, рух рівноприскорений.  

x(t)=10+9t+2,5t^2

Швидкість є похідною від координати тіла:

x'(t)=v(t)=9+2,5·2t=9+5t

v(10)=9+5·10=59 м/с

Прискорення є похідною від швидкості:

v'(t)=a(t)=5 м/с²

v₀(t)=v(0)=9 м/с

З рівняння залежності переміщення тіла від часу знайдемо s:

s(t)=v₀t+(at²)/2

s(t)=9·10+(5·10²)/2 = 90+(5·100)/2 = 90+250 = 340 м

Объяснение:

Answer 2

Equation of Motion:

The equation of motion for the body with coordinates x is given by x = 10t + 2t^2, where t represents time. This equation describes the position of the body as a function of time.

Velocity Equation:

To find the velocity equation, we need to differentiate the equation of motion with respect to time. The derivative of x with respect to t gives us the velocity v.

Differentiating x = 10t + 2t^2 with respect to t, we get:

v = dx/dt = 10 + 4t

Therefore, the velocity equation for the body is v = 10 + 4t.

Graph of Velocity:

To graph the dependence of velocity on time, we can plot the velocity equation v = 10 + 4t on a graph with time (t) on the x-axis and velocity (v) on the y-axis. The graph will be a straight line with a positive slope of 4, indicating that the velocity of the body is increasing linearly with time.

Acceleration Equation:

To find the acceleration equation, we need to differentiate the velocity equation with respect to time. The derivative of v with respect to t gives us the acceleration a.

Differentiating v = 10 + 4t with respect to t, we get:

a = dv/dt = 4

Therefore, the acceleration equation for the body is a = 4.

Graph of Acceleration:

The acceleration of the body is constant and equal to 4. This means that the body is experiencing a constant acceleration of 4 units per second squared. The graph of acceleration will be a horizontal line at a height of 4 on the y-axis, indicating that the acceleration remains constant over time.

Graph of Velocity and Acceleration:

To graph the dependence of velocity and acceleration on time, we can plot the velocity equation v = 10 + 4t and the acceleration equation a = 4 on the same graph. The graph will show the velocity as a linearly increasing line and the acceleration as a horizontal line at a height of 4.

Please note that the specific values of time, velocity, and acceleration will depend on the chosen range for the graph.