Respuesta :
Given:
The acceleration varies inversely with its mass.
When:
mass = 2 kg, the acceleration = 10 m/s²
Let's find the mass when the acceleration is 4 m/s².
Since the acceleration of the object varies inversely with its mass, we have the equation:
[tex]a=\frac{k}{m}[/tex]Where:
a is the acceleration
m is the mass
k is the constant of variation.
When m = 2, a = 10:
[tex]10=\frac{k}{2}[/tex]Now, let's find k.
Multiply both sides by 2
[tex]\begin{gathered} 10*2=\frac{k}{2}*2 \\ \\ 20=k \\ \\ k=20 \end{gathered}[/tex]Now, the equation which represents this variation is:
[tex]a=\frac{20}{m}[/tex]Now, to find the mass when acceleration is 4 m/s², substitute 4 for a and solve for m.
We have:
[tex]\begin{gathered} 4=\frac{20}{m} \\ \\ m=\frac{20}{4} \\ \\ m=5 \end{gathered}[/tex]Therefore, when the acceleration is 4 m/s², the mass of the object is 5 kg.
• ANSWER:
5 kg
