SOlve the formula h=54t+1/2at$$ ^2 $$ for a

To solve the formula $ h = 54t + \frac{1}{2}at^2 $ for $ a $, follow these steps:

1. Start with the given formula:
   \[
   h = 54t + \frac{1}{2}at^2
   \]

2. Subtract $ 54t $ from both sides to isolate the term with $ a $:
   \[
   h - 54t = \frac{1}{2}at^2
   \]

3. To eliminate the fraction, multiply both sides by 2:
   \[
   2(h - 54t) = at^2
   \]

4. Finally, divide both sides by $ t^2 $ to solve for $ a $:
   \[
   a = \frac{2(h - 54t)}{t^2}
   \]

So, the formula for $ a $ is:
\[
a = \frac{2(h - 54t)}{t^2}
\]

Would you like more details on any step or have any questions?

Here are 5 related questions for practice:
1. If $ h = 100 $ and $ t = 5 $, what is $ a $?
2. How would you rearrange the formula to solve for $ t $ instead of $ a $?
3. What happens to $ a $ if $ h $ is doubled but $ t $ remains the same?
4. What is the physical significance of the formula $ h = 54t + \frac{1}{2}at^2 $?
5. How can you verify the correctness of the formula $ a = \frac{2(h - 54t)}{t^2} $ by substituting it back into the original equation?

**Tip:** When manipulating formulas, be careful with the distribution of operations, especially when dealing with fractions and exponents.

Learn how to solve the kinematic equation h = 54t + 1/2at^2 for acceleration (a) with a step-by-step solution. This problem involves algebraic manipulation and kinematic concepts. Suitable for high school students.

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