Newton's second law of motion and its 10 mathematical problems with solutions

1. Problem: A force of 50 N is applied to an object of mass 10 kg. Calculate the acceleration of the object.

   • Solution: Using $𝐹=𝑚𝑎$, where $𝐹=50\text{N}$ and $𝑚=10\text{kg}$, we have $𝑎=\frac{𝐹}{𝑚}=\frac{50\text{N}}{10\text{kg}}=5{\text{m/s}}^2$.

2. Problem: If a force of 100 N is applied to an object of mass 5 kg, what is the resulting acceleration?

   • Solution: Using $𝐹=𝑚𝑎$, where $𝐹=100\text{N}$ and $𝑚=5\text{kg}$, we have $𝑎=\frac{𝐹}{𝑚}=\frac{100\text{N}}{5\text{kg}}=20{\text{m/s}}^2$.

3. Problem: A 2 kg object experiences an acceleration of $6{\text{m/s}}^2$ under the influence of an unknown force. Determine the magnitude of the force.

   • Solution: Using $𝐹=𝑚𝑎$, where $𝑚=2\text{kg}$ and $𝑎=6{\text{m/s}}^2$, we have $𝐹=(2\text{kg})\times (6{\text{m/s}}^2)=12\text{N}$.

4. Problem: An object of mass 8 kg accelerates at $4{\text{m/s}}^2$ due to a force. Calculate the magnitude of the force.

   • Solution: Using $𝐹=𝑚𝑎$, where $𝑚=8\text{kg}$ and $𝑎=4{\text{m/s}}^2$, we have $𝐹=(8\text{kg})\times (4{\text{m/s}}^2)=32\text{N}$.

5. Problem: A force of 30 N is applied to an object, causing it to accelerate at $3{\text{m/s}}^2$. Determine the mass of the object.

   • Solution: Using $𝐹=𝑚𝑎$, where $𝐹=30\text{N}$ and $𝑎=3{\text{m/s}}^2$, we rearrange the formula to find $𝑚$: $𝑚=\frac{𝐹}{𝑎}=\frac{30\text{N}}{3{\text{m/s}}^2}=10\text{kg}$.

6. Problem: An object of mass 6 kg experiences an acceleration of $2{\text{m/s}}^2$ due to an applied force. What is the magnitude of the force?

   • Solution: Using $𝐹=𝑚𝑎$, where $𝑚=6\text{kg}$ and $𝑎=2{\text{m/s}}^2$, we have $𝐹=(6\text{kg})\times (2{\text{m/s}}^2)=12\text{N}$.

7. Problem: A force of 80 N acts on an object, causing it to accelerate at $10{\text{m/s}}^2$. Determine the mass of the object.

   • Solution: Using $𝐹=𝑚𝑎$, where $𝐹=80\text{N}$ and $𝑎=10{\text{m/s}}^2$, we rearrange the formula to find $𝑚$: $𝑚=\frac{𝐹}{𝑎}=\frac{80\text{N}}{10{\text{m/s}}^2}=8\text{kg}$.

8. Problem: An object of mass 12 kg experiences a force of 36 N. Calculate the acceleration of the object.

   • Solution: Using $𝐹=𝑚𝑎$, where $𝐹=36\text{N}$ and $𝑚=12\text{kg}$, we rearrange the formula to find $𝑎$: $𝑎=\frac{𝐹}{𝑚}=\frac{36\text{N}}{12\text{kg}}=3{\text{m/s}}^2$.

9. Problem: A force of 50 N accelerates an object at $5{\text{m/s}}^2$. Determine the mass of the object.

   • Solution: Using $𝐹=𝑚𝑎$, where $𝐹=50\text{N}$ and $𝑎=5{\text{m/s}}^2$, we rearrange the formula to find $𝑚$: $𝑚=\frac{𝐹}{𝑎}=\frac{50\text{N}}{5{\text{m/s}}^2}=10\text{kg}$.

10. Problem: An object of mass 15 kg experiences an acceleration of $3{\text{m/s}}^2$. Calculate the magnitude of the force acting on the object.

    • Solution: Using $𝐹=𝑚𝑎$, where $𝑚=15\text{kg}$ and $𝑎=3{\text{m/s}}^2$, we have $𝐹=(15\text{kg})\times (3{\text{m/s}}^2)=45\text{N}$.

These problems demonstrate the application of Newton's second law of motion in calculating the relationship between force, mass, and acceleration.