Question

for a moving object, the force acting on the object varies directly with the objects acceleration. when a force of 24n acts on a certain object, the acceleration of the object is 6\\(\frac{m}{2s}\\). if the force is changed to 36n, what will be the acceleration of the object?

Explanation:

Step1: Find the mass of the object

According to Newton's second law \(F = ma\). When \(F = 24N\) and \(a=\frac{6}{2}m/s^{2}=3m/s^{2}\), we can find the mass \(m\) using the formula \(m=\frac{F}{a}\).
\(m=\frac{24}{3}=8kg\)

Step2: Calculate the new acceleration

When the force \(F'=36N\) and mass \(m = 8kg\), again using \(F=ma\) (now \(a'=\frac{F'}{m}\))
\(a'=\frac{36}{8}=\frac{9}{2}m/s^{2} = 4.5m/s^{2}\)

Answer:

\(4.5m/s^{2}\)