Explanation:
[tex]F=ma[/tex]
The force is directly proportional to mass and acceleration.
a) If force is doubled then acceleration is doubled.
b) If mass is halved then acceleration of the will increase if the force is constant.
c) If the force is doubled and the mass is doubled then acceleration is halved.
[tex]F_1=m_1a_1\\\Rightarrow a_1=\frac{F_1}{m_1}[/tex]
[tex]2F_1=2(2m_1)a_2\\\Rightarrow F_1=2m_1a_2\\\Rightarrow a_2=\frac{F_1}{2m_1}[/tex]
Dividing the equation
[tex]\frac{a_1}{a_2}=\frac{\frac{F_1}{m_1}}{\frac{F_1}{2m_1}}\\\Rightarrow a_2=\frac{1}{2}a_1[/tex]
d) If the force is doubled and the mass is halved then acceleration is doubled
[tex]F_1=m_1a_1\\\Rightarrow a_1=\frac{F_1}{m_1}[/tex]
[tex]2F_1=2(\frac{m_1}{2})a_2\\\Rightarrow a_2=2\frac{F_1}{m_)}\\\Rightarrow a_2=\frac{F_1}{2m_1}[/tex]
e) If the force is halved then the acceleration is halved.
f) If the mass is doubled then the acceleration is halved keeping the constant force
g) If the force is halved and the mass is halved then the acceleration is doubled
[tex]F_1=m_1a_1\\\Rightarrow a_1=\frac{F_1}{m_1}[/tex]
[tex]\frac{1}{2}F_1=\frac{1}{2}(\frac{m_1}{2})a_2\\\Rightarrow a_2=2\frac{F_1}{m_1}[/tex]
h) If the force is halved and the mass is doubled then the acceleration is halved.
[tex]F_1=m_1a_1\\\Rightarrow a_1=\frac{F_1}{m_1}[/tex]
[tex]\frac{1}{2}F_1=\frac{1}{2}(2m_1)a_2\\\Rightarrow a_2=\frac{F_1}{2m_1}[/tex]
