Question

for a moving object, the force acting on the object varies directly with the object’s acceleration. when a force of 15 n acts on a certain object, the acceleration of the object is 3 m/s². if the force is changed to 10 n, what will be the acceleration of the object?

Explanation:

Step1: Recall Newton's Second Law (F = ma)

Since force \( F \) varies directly with acceleration \( a \), we can write \( F = k a \) (where \( k \) is the constant of proportionality, which is the mass \( m \) here). First, find the mass using the given force and acceleration. Given \( F_1 = 15 \, \text{N} \) and \( a_1 = 3 \, \text{m/s}^2 \), from \( F = ma \), we get \( m=\frac{F_1}{a_1} \).
\[ m = \frac{15}{3} = 5 \, \text{kg} \]

Step2: Calculate new acceleration with new force

Now, the new force \( F_2 = 10 \, \text{N} \) and mass \( m = 5 \, \text{kg} \) (mass is constant). Using \( F = ma \), we solve for \( a_2 \): \( a_2=\frac{F_2}{m} \).
\[ a_2 = \frac{10}{5} = 2 \, \text{m/s}^2 \]

Answer:

The acceleration of the object will be \( 2 \, \text{m/s}^2 \).