Answer to Question #166767 in Physics for Sky

Question

As we will learn, kinetic energy ( K ) has units kg•m 2 /s 2 . If we represent the mass of an object with

m and its speed with v , we can write the kinetic energy as K = Am b v c , where A is a unitless

constant. (a) What must the values of b and c be? (b) Now, we are given an equation for kinetic

energy of an object that reads K = D + Am b v c . What can you say about the units of D ? (c) What

sort of quantity must D be?

Would it be possible to explain in steps, please?

Answer 1

a)

$$[K]=[A][m]^b[v]^c\\ML^2T^{-2}=1\cdot[M]^b[LT^{-1}]^c\\b=1\\c=2$$

b)

$$[K]=[D]+[A][m]^b[v]^c\\ML^2T^{-2}=[D]$$

Units:

$$kg\frac{m^2}{s^2}$$

c) Energy.