Calculating Angular Position from Time Equation

The question provides an equation that describes the angular motion of a disc. The equation for the angular position, denoted by $\theta$, is given as a function of time $t$. We need to find the angular position of the disc at a specific time, which is $t = 2$ seconds.

The given relation for angular position is:

$\theta = 3t + t^3$

Here, $\theta$ is measured in radians and $t$ is measured in seconds.

We want to find the value of $\theta$ when $t = 2$ seconds. To do this, we substitute $t=2$ into the given equation.

Substitute $t = 2$ seconds into the equation:

$\theta(t=2) = 3(2) + (2)^3$

Now, we calculate the terms:

First term: $3 \times 2 = 6$

Second term: $(2)^3 = 2 \times 2 \times 2 = 8$

Now, add the calculated terms to find the total angular position at $t=2$ seconds:

$\theta(t=2) = 6 + 8$

$\theta(t=2) = 14$

Since $\theta$ is in radians, the angular position after 2 seconds is 14 radians.

Therefore, at $t = 2$ seconds, the angular position of the disc is 14 radians.