Question

[The angular displacement of a particle is given by
Theta=W(Omega)t+ 1/2 alpha t^2]

Omega=1Rad/s
Alpha =1.5 Rad\s^2
angular velocity at time t=2sec will be (in Radian per second) ?????​

Answer 1

Ф = ωt+$\frac{1}{2}$α$t^{2}$

$\frac{d}{dt}$Ф = ω + αt

angular vel at t = 2 => 1 + 1.5x2 = 4

Answer 2

Answer:

4 rad / sec

Explanation:

Given :

$\displaystyle{\theta=\omega_0+1/2\alpha \ t^2}$

ω = 1 rad / sec

α = 1.5 rad / sec²

We have find angular velocity :

we have that angular velocity ( ω) is given by :

$\displaystyle{\omega=\dfrac{d\theta}{dt}}\\\\\\\displaystyle{\omega=\dfrac{d}{dt}\left(\omega_0t+1/2 \ \alpha \ t^2\right)}\\\\\\\displaystyle{\omega=\omega_0+1\times2/2 \ \alpha \ t}\\\\\\\displaystyle{\omega=\omega_0+\alpha \ t}$

Putting given values :

ω = 1 + 1.5 × 2  rad / sec

ω = 1 + 3 rad / sec

ω = 4 rad / sec

Thus we get answer 4 rad / sec .