Question

X y

2 5
4 10
6 15
8 20


Object A and Object B are two objects in motion. Given the table of Object A and the equation y =
18
5
x of Object B, which of the two moving objects has greater speed and by what factor? (round to nearest hundredth)
A) Object A by a factor of 1.10
B) Object B by a factor of 1.10
C) Object A by a factor of 1.44
D) Object B by a factor of 1.44

Answer 1

The Answer is D:Object B by a factor of 1.44

Object A: 5/2 = 2.5
Object B: 18/5 = 3.6

That being so
3.6/2.5 = 1.44

You're Welcome.

Answer 2

D) Object B is faster by a factor of 1.44

Explanation:

Using the table for Object A, we will find the equation representing its motion.

Since, slope =
`(10-5)/(4-2)=(5)/(2)`

So, substituting the slope and (2,5) in the equation 'y=mx+b', where m= slope, we get,

`5=(5)/(2)* 2+b` i.e. b = 0

So, the equation for the motion of Object A is,
`y=(5)/(2)x`

Also, the equation for the motion of Object B is,
`y=(18)/(5)x`

That is,

Speed of Object A =
`(5)/(2)=2.5`

Speed of Object B =
`(18)/(5)=3.6`

So, the factor of increase in the speed =
`(3.6)/(2.5)` = 1.44

Hence, Object B is faster by a factor of 1.44.

Thus, option D is correct.