Question

Угол α, на который поворачивается колесо за t сек., равне α=at^2-bt+c, где a,b,c - положительные константы. Найти угловую скорость V движения колеса. Через сколько времени от начала движения угловая скорость будет равна нулю?

Answer 1

$V(t)=\frac{d\alpha}{dt}$

$V(t)=2a t-b$

$0=2a t-b$

$t=\frac{b}{2a}$

Answer 2

Calculation of Angular Velocity

To find the angular velocity V of the wheel, we need to differentiate the equation for the angle α with respect to time t. The equation for α is given as:

α = at^2 - bt + c

Differentiating this equation with respect to t, we get:

dα/dt = 2at - b

Therefore, the angular velocity V of the wheel is given by V = dα/dt = 2at - b.

Time when Angular Velocity is Zero

To find the time when the angular velocity V is zero, we need to set V = 0 and solve for t.

Setting V = 0, we have:

2at - b = 0

Solving for t, we get:

t = b / (2a)

Therefore, the time when the angular velocity is zero is t = b / (2a).

Please note that the values of a and b are positive constants, as mentioned in the question.

I hope this helps! Let me know if you have any further questions.