The angular displacement of a body on a circular orbit is given by the function:

Question

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The angular displacement of a body on a circular orbit is given by the function:

\theta(t) = 2t^2 + 5t + 5

where $t$ is in seconds.

To calculate the angular velocity, we need to find the derivative of the angular displacement with respect to time. Angular velocity $\omega(t)$ is defined as $\omega(t) = \frac{d\theta}{dt}$ .

Differentiate the angular displacement function with respect to time.
$\omega(t) = \frac{d}{dt}(2t^2 + 5t + 5)$ $\omega(t) = \frac{d}{dt}(2t^2) + \frac{d}{dt}(5t) + \frac{d}{dt}(5)$ $\omega(t) = 2(2t) + 5(1) + 0$ $\omega(t) = 4t + 5$
Substitute $t = 2 \text{ s}$ into the angular velocity function.
$\omega(2) = 4(2) + 5$ $\omega(2) = 8 + 5$ $\omega(2) = 13 \text{ rad/s}$
The angular velocity at $t = 2 \text{ s}$ is $\boxed{13 \text{ rad/s}}$ .

The angular displacement of a body on a circular orbit is given by the function:

Answer

Step-by-step solution

Differentiate the angular displacement function with respect to time.

Substitute $t = 2 \text{ s}$ into the angular velocity function.

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The angular displacement of a body on a circular orbit is given by the function:

Answer

Step-by-step solution

Differentiate the angular displacement function with respect to time.

Substitute t=2 st = 2 \text{ s}t=2 s into the angular velocity function.

Try one yourself

Still stuck on this one?

More Computer Science Questions

Substitute $t = 2 \text{ s}$ into the angular velocity function.