# Basic Conversion from Translational Motion Equation

• TrueBlood
In summary, the equation t = sqrt(2h/g) is derived from the standard translational motion equations by manipulating the equation h = Vot + 1/2g(t)^2. However, the equation t = Vo*sqrt(2h/g) is incorrect as it has different dimensions. The correct equation for finding the range is r = Vot, and t = sqrt(2h/g) can be used when t is not given.
TrueBlood
Studying for the MCAT, and trying to figure out how t = sqrt(2h/g) and t = Vo*sqrt(2h/g) is derived from the standard translational motion equations.

h = change in h
t = change in t

thus...

h = Vot + 1/2g(t)^2
h - Vot = 1/2g(t)^2
(2h)/g - (2Vot)/g =t^2
sqrt(2h/g) - sqrt(2Vot)/g = t

Obviously, I don't know how to simplify it further.

Thanks.

TrueBlood said:
Studying for the MCAT, and trying to figure out how t = sqrt(2h/g) and t = Vo*sqrt(2h/g) is derived from the standard translational motion equations.
Those equations cannot both be correct--they have different dimensions!

Only the first is correct, and only when Vo = 0.

TrueBlood said:
h = Vot + 1/2g(t)^2
h - Vot = 1/2g(t)^2
(2h)/g - (2Vot)/g =t^2
sqrt(2h/g) - sqrt(2Vot)/g = t
Also realize that your last step is mathematically incorrect:

$$\sqrt{a^2 - b^2} \ne a - b$$

For example sqrt(5^2 - 3^2) = sqrt(16) = 4 ≠ 5 - 3

The last step, mathematically correct, would be...

sqrt[(2h-2Vot)/g] = t

and in a free-fall equation, where Vo = 0, then t = sqrt(2h/g)

I found out t = Vo*sqrt(2h/g) when you are trying to find the range (r = Vot) and using t = sqrt(2h/g) when you don't have t.
Thx.

TrueBlood said:
The last step, mathematically correct, would be...

sqrt[(2h-2Vot)/g] = t

and in a free-fall equation, where Vo = 0, then t = sqrt(2h/g)
Good.

I found out t = Vo*sqrt(2h/g) when you are trying to find the range (r = Vot) and using t = sqrt(2h/g) when you don't have t.
Careful. That equation as written makes no sense. You probably meant to use r instead of t. And t = sqrt(2h/g) would only be half the time for the full trajectory.

## 1. What is translational motion and why is it important?

Translational motion refers to the movement of an object from one point to another in a straight line. It is important because it helps us understand and describe the motion of objects in our daily lives, as well as in scientific studies.

## 2. What is the equation for translational motion?

The equation for translational motion is distance = velocity x time, or d = vt. This equation can be used to calculate the distance an object travels in a given amount of time, if its velocity is known.

## 3. How do I convert units in the translational motion equation?

To convert units in the translational motion equation, you can use conversion factors. For example, if you need to convert from meters per second (m/s) to kilometers per hour (km/h), you can multiply the value by 3.6, as 1 km/h = 3.6 m/s.

## 4. Can the translational motion equation be used for objects with changing velocities?

Yes, the translational motion equation can be used for objects with changing velocities. However, the velocity used in the equation would need to be the average velocity over the given time period.

## 5. How is the translational motion equation related to other equations of motion?

The translational motion equation is a simplified version of the more general equations of motion, which take into account factors such as acceleration. It can be derived from these equations by assuming a constant velocity and no acceleration.

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