Question

the position function of a golf ball rolling on an incline is given by (d(t) = 4t^2 + 5t), where (d) is measured in meters, (t) in seconds. find the balls velocity at (t = 3) seconds.

Explanation:

Relate velocity to position

$$ v(t) = d'(t) = \frac{d}{dt}(4t^2 + 5t) $$

Differentiate the position function

$$ v(t) = 8t + 5 $$

Evaluate the velocity at t = 3

$$ v(3) = 8(3) + 5 = 29 $$

Answer:

The position function of a golf ball rolling on an incline is given by \(d(t) = 4t^2 + 5t\), where \(d\) is measured in meters, \(t\) in seconds. Find the ball's velocity at \(t = 3\) seconds.

Answer: <blank>29</blank> m/s