Question

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

Explanation:

Find the velocity function by differentiating position

$$ v(t) = d'(t) = \frac{d}{dt}(3t^2 + 2t) = 6t + 2 $$

Find the acceleration function by differentiating velocity

$$ a(t) = v'(t) = \frac{d}{dt}(6t + 2) = 6 $$

Evaluate the acceleration at the given time

$$ a(4) = 6\text{ m/s}^2 $$

Answer:

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

Answer: <blank>6</blank> \(\text{m/s}^2\)