Question

Тело движется прямолинейно в вертикальном направлении по закону h(t)=2+9t-4t2 (t - время движения в секундах, h - расстояние в метрах от земли до тела). Определите скорость (в м/с) через 1 секунду после начала движения.

Answer 1

Скорость это первая производная от расстояния:

v=h'=9-8t

Теперь подставляем t=1:

v=9-8=1м/с

 

 

 

 

 

 

 

 

 

 

Answer 2

Calculation of Velocity

To determine the velocity of the body after 1 second of motion, we need to find the derivative of the height function h(t) with respect to time t. The derivative of h(t) represents the rate of change of height with respect to time, which is the velocity.

The given height function is h(t) = 2 + 9t - 4t^2, where t represents the time in seconds and h represents the height in meters.

To find the derivative of h(t), we can differentiate each term of the function separately:

- The derivative of the constant term 2 is 0. - The derivative of the term 9t is 9. - The derivative of the term -4t^2 is -8t.

Adding these derivatives together, we get the derivative of h(t):

h'(t) = 0 + 9 - 8t = 9 - 8t

Now, we can substitute t = 1 into the derivative to find the velocity after 1 second:

h'(1) = 9 - 8(1) = 9 - 8 = 1

Therefore, the velocity of the body after 1 second of motion is 1 m/s.