1. The variables x and y vary directly. When x is 3, y is 6. Find x when y = 2/3.
2. The force acting on an object varies directly with its acceleration. A force of 25
newtons accelerates an object at 1.25 m/s. What is the acceleration of a 35
newton force?
Please help this assignment is very confusing
y = k x
6 = 3 k
k = 2
y = 2 x
2/3 = 2 x
x = 2/6 = 1/3
=================
25 = m (1.25)
so
m = 25/1.25
a = F/m = 35 /(25/1.25)
= 1.25 * (35/25)=1.75
You could have written that down immediately by proportions but:
1. I am a physicist
2. You are doing algebra of direct variation.
To solve these problems, we can use the concept of direct variation, which states that two variables are directly proportional to each other if their ratio remains constant. We can represent this relationship using an equation in the form of y = kx, where y and x are the variables, and k is the constant of variation.
1. Given that x and y vary directly, and when x is 3, y is 6, we can plug these values into the equation and solve for k:
6 = k * 3
Divide both sides by 3:
2 = k
So, the equation for direct variation is y = 2x.
Now, we need to find the value of x when y is 2/3. Substituting this in the equation, we get:
2/3 = 2x
Multiply both sides by 3 to isolate x:
2 = 6x
Divide both sides by 6:
2/6 = x
Simplifying the fraction, we get:
x = 1/3
Therefore, when y = 2/3, x = 1/3.
2. Similarly, using the concept of direct variation, we can write the equation for direct variation as F = ka, where F is the force, a is the acceleration, and k is the constant of variation.
Given that a force of 25 newtons accelerates an object at 1.25 m/s, we can plug these values into the equation to solve for k:
25 = k * 1.25
Divide both sides by 1.25:
k = 25 / 1.25
k = 20
Now, we need to find the acceleration when the force is 35 newtons. Substituting this in the equation, we get:
35 = 20a
Divide both sides by 20:
35 / 20 = a
Simplifying the fraction, we get:
a = 1.75 m/s
Therefore, when the force is 35 newtons, the acceleration is 1.75 m/s.