hamed7299
Answered

At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

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 appreciate your time. Please come back anytime for the latest information and answers to your questions. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.