Please tell me how to set this up...
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?
force=k*acceleration.
25=k*1.25m/s^2
k=25/1.25=20
35=20*a
a=1.75m/s^2
To solve this problem, we need to use the concept of direct variation. In direct variation, two variables are directly proportional to each other when one variable is a constant multiple of the other.
In this case, the force and acceleration are directly proportional. Let's denote the force as F and the acceleration as a. According to the problem, we have the following information:
Force (F) = 25 newtons
Acceleration (a) = 1.25 m/s
To find the constant of proportionality, we divide the force by the acceleration:
Constant of proportionality = F / a
Substituting the given values into the formula:
Constant of proportionality = 25 newtons / 1.25 m/s
Now, we have the constant of proportionality, which we can use to find the acceleration for a different force.
Force (F) = 35 newtons
To find the acceleration (a), we multiply the force by the constant of proportionality:
Acceleration (a) = F * (Constant of proportionality)
Substituting the values into the formula:
Acceleration (a) = 35 newtons * (25 newtons / 1.25 m/s)
Simplifying the expression:
Acceleration (a) = 35 newtons * (20 m/s)
Acceleration (a) = 700 m/s
Therefore, the acceleration for a 35 newton force is 700 m/s.