Question

the position function of a golf ball rolling on an incline is given by (d(t) = 5t^2 + 7t), where (d) is measured in meters, (t) in seconds. find the balls velocity at (t = 3) seconds.

Explanation:

Relate velocity to the position function

Using the Position and Velocity Relations knowledge point

$$ v(t) = d'(t) = \frac{d}{dt}[5t^2 + 7t] $$

Differentiate the position function

Using the Power Rule Differentiation knowledge point

$$ v(t) = 10t + 7 $$

Evaluate the velocity at the given time

Using the Position and Velocity Relations knowledge point

$$
LATEXBLOCK0
$$

Answer:

The position function of a golf ball rolling on an incline is given by \(d(t) = 5t^2 + 7t\), where \(d\) is measured in meters, \(t\) in seconds. Find the ball's velocity at \(t = 3\) seconds.

Answer: <blank>37</blank> \(\text{m/s}\)