Question

Тіло рухається за законом S=4t²-16t+4 . У який момент часу швидкість руху дорівнює 0?

Answer 1

Ответ:

найдем и приравняем v=8t-16==0, t=16/8=2c

Answer 2

Finding the Time When Velocity is Zero

To find the time when the velocity of the object is zero, we need to determine the value of 't' that makes the velocity equation equal to zero.

The given equation for velocity is: V(t) = 4t² - 16t + 4.

To find the time when the velocity is zero, we need to solve the equation V(t) = 0.

Let's set up the equation and solve for 't':

4t² - 16t + 4 = 0

To solve this quadratic equation, we can use the quadratic formula:

t = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 4, b = -16, and c = 4.

Substituting these values into the quadratic formula, we get:

t = (-(-16) ± √((-16)² - 4 * 4 * 4)) / (2 * 4)

Simplifying further:

t = (16 ± √(256 - 64)) / 8

t = (16 ± √192) / 8

Now, let's calculate the values of 't':

t₁ = (16 + √192) / 8

t₂ = (16 - √192) / 8

Calculating the values:

t₁ ≈ 3.46

t₂ ≈ 0.54

Therefore, the velocity of the object is equal to zero at approximately t = 0.54 and t = 3.46.

Please note that these values are approximate and rounded to two decimal places.