Question

Which distance formula or formulas show(s) a joint variation?

i) d=50t
ii) d=1/2gt²
iii) d=rt
A) i) only
B) ii) only
C) iii) only
D) i) and ii)

Answer 1

The correct answer is Option B, which is the formula ii) d=1/2gt², as it shows distance varies with both gravity and time squared, demonstrating a joint variation.

Step-by-step explanation:

The question asks which distance formula or formulas demonstrate a joint variation. Joint variation means that the distance d changes in proportion to more than one factor.

1. Formula i) d=50t shows that d varies directly with time t but involves only one variable.
2. Formula ii) d=1/2gt² indicates that d varies jointly with gravity g and time squared t².
3. Formula iii) d=rt suggests that d varies directly with rate r and time t, but like in i), it's not a joint variation with respect to a second independent variable.

Option B is the correct answer because formula ii) shows that d varies with two different factors, g and t, thus demonstrating joint variation.

Joint variation occurs when a variable depends on the product of two or more other variables, often expressed as (y = kxz), where (k) is a constant. Examining the provided distance formulas:

i) (d = 50t) - This formula shows direct variation, not joint variation, as the distance (d) is directly proportional to time (t).

ii) (d=1/2gt²) - This formula represents distance traveled under constant acceleration due to gravity. It exhibits joint variation, involving both time (t) and gravitational acceleration (g), making option B) ii) the correct choice.

iii) (d = rt) - This is a linear equation indicating direct variation between distance 9d) and time (t), not joint variation.

Therefore, the correct answer is B) ii) only, as it specifically demonstrates joint variation with d depending on both t and g.