Solve?? Help

Question

1. Kinetic energy, K, equals the product of 1/2, the mass of an object, m, and the square of its velocity, v. Write a formula for kinetic energy. Then solve your formula for v.

 

2. In a circle, area and circumference can be found using the formulas A=πr² and C=2πr, respectively. Write a formula for C in terms of A (Your answer should not contain π.)

Answer 1

K= 1/2 mv²

 

v² =2K/m

 

v= √(2K/m)

 

 

A= π r²       C= 2π r     r= C/2π

Thus, A = π x (C/2π)²  

            = π x C²/4π² 

            = C²/4π

Thus C² = 4Aπ     C =2√(Aπ)

Answer 2

1. Formula for kinetic energy: K = (1/2)*mv²

Correspondingly, v= √2k/m

 

2. Let's notice, that A/C = πr²/2πr = r/2

Therefore, C = 2A/r