Math solution on Newton’s second law

 Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass. The formula is often written as:

$𝐹=𝑚𝑎$

where $𝐹$ is the net force acting on the object, $𝑚$ is the mass of the object, and $𝑎$ is the acceleration of the object. Here are 20 problems involving Newton's Second Law, along with their solutions:

Problem 1

Problem: A 5 kg object is subjected to a net force of 20 N. What is its acceleration?

Solution: $𝑎=\frac{𝐹}{𝑚}=\frac{20\text{N}}{5\text{kg}}=4{\text{m/s}}^2$

Problem 2

Problem: A car with a mass of 1500 kg accelerates at a rate of 2 m/s². What is the net force acting on the car?

Solution: $𝐹=𝑚𝑎=1500\text{kg}\times 2{\text{m/s}}^2=3000\text{N}$

Problem 3

Problem: An object experiences a net force of 45 N and accelerates at 9 m/s². What is its mass?

Solution: $𝑚=\frac{𝐹}{𝑎}=\frac{45\text{N}}{9{\text{m/s}}^2}=5\text{kg}$

Problem 4

Problem: A 10 kg object is accelerating at 3 m/s². Find the net force acting on the object.

Solution: $𝐹=𝑚𝑎=10\text{kg}\times 3{\text{m/s}}^2=30\text{N}$

Problem 5

Problem: A net force of 16 N is applied to a 4 kg mass. What is the acceleration of the mass?

Solution: $𝑎=\frac{𝐹}{𝑚}=\frac{16\text{N}}{4\text{kg}}=4{\text{m/s}}^2$

Problem 6

Problem: A force of 50 N is needed to give an object an acceleration of 5 m/s². Find the mass of the object.

Solution: $𝑚=\frac{𝐹}{𝑎}=\frac{50\text{N}}{5{\text{m/s}}^2}=10\text{kg}$

Problem 7

Problem: A 3 kg object accelerates at 7 m/s². What is the magnitude of the net force acting on the object?

Solution: $𝐹=𝑚𝑎=3\text{kg}\times 7{\text{m/s}}^2=21\text{N}$

Problem 8

Problem: If a net force of 12 N is applied to a 3 kg object, what is the acceleration produced?

Solution: $𝑎=\frac{𝐹}{𝑚}=\frac{12\text{N}}{3\text{kg}}=4{\text{m/s}}^2$

Problem 9

Problem: An object with a mass of 8 kg is subjected to a force of 32 N. Find the acceleration of the object.

Solution: $𝑎=\frac{𝐹}{𝑚}=\frac{32\text{N}}{8\text{kg}}=4{\text{m/s}}^2$

Problem 10

Problem: A net force of 60 N acts on a 15 kg object. What is its acceleration?

Solution: $𝑎=\frac{𝐹}{𝑚}=\frac{60\text{N}}{15\text{kg}}=4{\text{m/s}}^2$

Problem 11

Problem: A 0.5 kg object is accelerated at a rate of 8 m/s² by a force. Calculate the force.

Solution: $𝐹=𝑚𝑎=0.5\text{kg}\times 8{\text{m/s}}^2=4\text{N}$

Problem 12

Problem: An object has a mass of 12 kg and a net force of 36 N is applied to it. What is the object's acceleration?

Solution: $𝑎=\frac{𝐹}{𝑚}=\frac{36\text{N}}{12\text{kg}}=3{\text{m/s}}^2$

Problem 13

Problem: If a 20 N force is applied to a 5 kg object, what is the resulting acceleration?

Solution: $𝑎=\frac{𝐹}{𝑚}=\frac{20\text{N}}{5\text{kg}}=4{\text{m/s}}^2$

Problem 14

Problem: An object has a mass of 9 kg and is accelerating at 2 m/s². Determine the force acting on it.

Solution: $𝐹=𝑚𝑎=9\text{kg}\times 2{\text{m/s}}^2=18\text{N}$

Problem 15

Problem: A 6 kg object experiences an acceleration of 3 m/s². What is the net force?

Solution: $𝐹=𝑚𝑎=6\text{kg}\times 3{\text{m/s}}^2=18\text{N}$

Problem 16

Problem: An object is subjected to a net force of 14 N and accelerates at 2 m/s². Find the mass of the object.

Solution: $𝑚=\frac{𝐹}{𝑎}=\frac{14\text{N}}{2{\text{m/s}}^2}=7\text{kg}$

Problem 17

Problem: A 0.2 kg object is acted upon by a net force of 1.6 N. What is the acceleration?

Solution: $𝑎=\frac{𝐹}{𝑚}=\frac{1.6\text{N}}{0.2\text{kg}}=8{\text{m/s}}^2$

Problem 18

Problem: An object with a mass of 10 kg accelerates at 5 m/s². Calculate the net force acting on it.

Solution: $𝐹=𝑚𝑎=10\text{kg}\times 5{\text{m/s}}^2=50\text{N}$

Problem 19

Problem: A net force of 24 N is applied to a 3 kg object. What is the object's acceleration?

Solution: $𝑎=\frac{𝐹}{𝑚}=\frac{24\text{N}}{3\text{kg}}=8{\text{m/s}}^2$

Problem 20

Problem: An object with a mass of 15 kg is accelerating at 4 m/s². Find the net force acting on the object.

Solution: $𝐹=𝑚𝑎=15\text{kg}\times 4{\text{m/s}}^2=60\text{N}$

These problems illustrate the application of Newton's Second Law in various contexts, helping to understand the relationship between force, mass, and acceleration.