The position of a golf ball is described by rr(t)=2t2. What is the velocity at t=3s?

The position of the golf ball is given by \( r(t) = 2t^2 \).

To find the velocity, we need to differentiate the position function \( r(t) \) with respect to time \( t \), as velocity is the derivative of position:

\[
v(t) = \frac{dr(t)}{dt} = \frac{d}{dt} \left( 2t^2 \right)
\]

Now, differentiate:

\[
v(t) = 2 \cdot \frac{d}{dt}(t^2) = 2 \cdot 2t = 4t
\]

Thus, the velocity as a function of time is:

\[
v(t) = 4t
\]

Now, to find the velocity at \( t = 3 \) seconds, we substitute \( t = 3 \) into the velocity function:

\[
v(3) = 4 \times 3 = 12 \, \text{m/s}
\]

So, the velocity at \( t = 3 \) seconds is \( 12 \, \text{m/s} \).

Would you like more details or have any questions?

Here are 5 related questions you can explore:
1. How would the velocity change if the position function was \( r(t) = 3t^2 \)?
2. What is the acceleration of the ball at any time \( t \)?
3. If the ball's position was described by \( r(t) = 2t^3 \), how would you calculate the velocity at \( t = 3 \) seconds?
4. What is the physical meaning of the derivative in terms of motion?
5. How do you calculate the average velocity over an interval?

**Tip:** The velocity function is always the derivative of the position function with respect to time.

The position of a golf ball is described by r(t)=2t^2. What is the velocity at t=3s?

Learn how to calculate the velocity of a golf ball described by the position function r(t) = 2t^2 at t=3 seconds. This problem involves applying calculus concepts such as derivatives and kinematics to solve for velocity. Suitable for students in Grades 11-12.

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