hamed7299
Answered

Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

Prove the correctness of this equation s=vt + 1/2at ​

Sagot :

MrRoyal

Answer:

The formula is dimensionally correct.

Explanation:

Given

[tex]s = ut + \frac{1}{2}at^2[/tex]

Required

Prove its correctness

Write out the dimension of each:

[tex]s = M^0LT^0[/tex] --- displacement

[tex]ut = M^0LT^{-1} * T[/tex] --- velocity * time

[tex]\frac{1}{2}at^2 = M^0LT^{-2} * T^2[/tex] --- acceleration * square of time

The expression becomes:

[tex]s = ut + \frac{1}{2}at^2[/tex]

[tex]M^0LT^0 = M^0LT^{-1} * T + M^0LT^{-2} * T^2[/tex]

Apply law of indices

[tex]M^0LT^0 = M^0LT^{-1+1} + M^0LT^{-2+2}[/tex]

[tex]M^0LT^0 = M^0LT^{0} + M^0LT^{0}[/tex]

[tex]M^0LT^0 = M^0LT^{0}[/tex]

Both sides of the equation are equal

We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.