Question

a constant force is applied to an object, causing the object to accelerate at 8.50 m/s². what will the acceleration be if
the force is doubled?
express your answer with the appropriate units.

part b
the objects mass is doubled?
express your answer with the appropriate units.

part c
the force and the objects mass are both doubled?
express your answer with the appropriate units.

Explanation:

Step1: Recall Newton's second - law

According to Newton's second - law, $F = ma$, where $F$ is the force, $m$ is the mass, and $a$ is the acceleration. Initially, $F_1=m_1a_1$, and $a_1 = 8.50\ m/s^{2}$.

Step2: Solve Part A (force is doubled)

If the force is doubled, $F_2 = 2F_1$ and the mass remains the same ($m_2=m_1$). From $F = ma$, we have $F_1=m_1a_1$ and $F_2=m_2a_2$. Substituting $F_2 = 2F_1$ and $m_2=m_1$ into $F_2=m_2a_2$ gives $2F_1=m_1a_2$. Since $F_1=m_1a_1$, then $2m_1a_1=m_1a_2$. Canceling out $m_1$ (since $m_1
eq0$), we get $a_2 = 2a_1$. So $a_2=2\times8.50\ m/s^{2}=17.0\ m/s^{2}$.

Step3: Solve Part B (mass is doubled)

If the mass is doubled, $m_2 = 2m_1$ and the force remains the same ($F_2=F_1$). From $F_1=m_1a_1$ and $F_2=m_2a_2$, substituting $F_2=F_1$ and $m_2 = 2m_1$ gives $F_1=2m_1a_2$. Since $F_1=m_1a_1$, then $m_1a_1=2m_1a_2$. Canceling out $m_1$ (since $m_1
eq0$), we get $a_2=\frac{a_1}{2}$. So $a_2=\frac{8.50}{2}\ m/s^{2}=4.25\ m/s^{2}$.

Step4: Solve Part C (force and mass are both doubled)

If $F_2 = 2F_1$ and $m_2 = 2m_1$. From $F_1=m_1a_1$ and $F_2=m_2a_2$, substituting $F_2 = 2F_1$ and $m_2 = 2m_1$ gives $2F_1=2m_1a_2$. Since $F_1=m_1a_1$, then $2m_1a_1=2m_1a_2$. Canceling out $2m_1$ (since $m_1
eq0$), we get $a_2=a_1$. So $a_2 = 8.50\ m/s^{2}$.

Answer:

Part A:
Value: 17.0
Units: $m/s^{2}$
Part B:
Value: 4.25
Units: $m/s^{2}$
Part C:
Value: 8.50
Units: $m/s^{2}$