# Kinematics Word Problem [closed]

A curling rink is approximately 35 m long from button to button. Mr. Grover releases a rock and 20. seconds later it stops on the far button. What was the initial velocity of the stone? What deceleration did it undergo?

• Initial velocity = ?
• Final velocity = 0 m/s
• Time = 20 seconds
• Acceleration = ?
• Distance = 35 m

Did I forget anything because I can't use any of the formulas I learned if I'm missing two things.

Formulas \begin{align} v_{f} &= v_{i} + at\\ v_{f}^2 &= v_{i}^2 + 2 ad\\ d &= v_{i} t + \frac12 at^2\\ a &= \frac{v_{f} - v_{i}}{t}\\ \end{align}

## closed as off-topic by John Rennie, Ali, Qmechanic♦Oct 17 '14 at 14:27

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• You're forgetting a couple average velocity equations. Find the average velocity of the stone over the time interval, and then use that and the final velocity to find an initial velocity – Sean Oct 17 '14 at 1:22

Use $d=v_i t +\frac{1}{2}a t^2$ and then substitute from the first equation that $v_i=-a t$. You get $$d= -at^2+\frac{1}{2}at^2=-\frac{1}{2}at^2$$ from which you can infer $$a=-\frac{2d}{t^2}$$ Once you have the acceleration you get the initial velocity from $v_i=-a t$.