An object will take t seconds to drop d feet, where t=\sqrt{d}/16. What distance will the object...

Question:

An object will take t seconds to drop d feet, where {eq}t=\sqrt{d}/16 {/eq}. What distance will the object drop in {eq}\sqrt{5}/2 {/eq}s?

Kinematic Equations

Kinematic equations describe relationships between an object's motion and time. Typically these are functions of time for velocity and position.

Answer and Explanation:

Given a relationship of:

{eq}t=\dfrac{\sqrt{d}}{16} {/eq}

We can rearrange to find a distance equation in dependent on time.

{eq}d=16^2t^2=256t^2 {/eq}

So after {eq}\sqrt{5}/2 {/eq} seconds, the object will have fallen:

{eq}d=256(\frac{\sqrt{5}}{2})^2=\boxed{1600 feet} {/eq}


Learn more about this topic:

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Solving Kinematics Problems

from NY Regents Exam - Physics: Test Prep & Practice

Chapter 2 / Lesson 21
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