Question

1. how much force is required to accelerate a 2 kg mass at 3 m/s²? given m = 2 kg, a = 3 m/s². answer: the force required to accelerate a 2 kg mass at 3 m/s² is 6 n. work: f=ma, f = 2 kg x 3 m/s² = 6 n. 2. given a force of 100 n and an acceleration of 10 m/s², what is the mass? given, answer, work. 3. what is the acceleration of a 10 kg mass pushed by a 5 n force? given, answer, work. 4. given a force of 88 n and an acceleration of 4 m/s², what is the mass? given, answer, work.

Explanation:

1. For the first - type problem (How much force is required to accelerate a 2 kg mass at 3 m/s²?):

• Explanation:
• Step 1: Recall Newton's second - law formula

The formula for Newton's second law is \(F = ma\), where \(F\) is the force, \(m\) is the mass, and \(a\) is the acceleration.

• Step 2: Substitute the given values

Given \(m = 2\ kg\) and \(a=3\ m/s^{2}\), we substitute these values into the formula \(F = ma\). So, \(F=2\ kg\times3\ m/s^{2}\).
\(F = 6\ N\).

• Answer: \(6\ N\)

1. For the second - type problem (Given a force of 100 N and an acceleration of 10 m/s², what is the mass?):

• Explanation:
• Step 1: Rearrange Newton's second - law formula

From \(F = ma\), we can solve for \(m\) by the formula \(m=\frac{F}{a}\).

• Step 2: Substitute the given values

Given \(F = 100\ N\) and \(a = 10\ m/s^{2}\), we substitute into \(m=\frac{F}{a}\). So, \(m=\frac{100\ N}{10\ m/s^{2}}\).
\(m = 10\ kg\).

• Answer: \(10\ kg\)

1. For the third - type problem (What is the acceleration of a 10 kg mass pushed by a 5 N force?):

• Explanation:
• Step 1: Rearrange Newton's second - law formula

From \(F = ma\), we can solve for \(a\) by the formula \(a=\frac{F}{m}\).

• Step 2: Substitute the given values

Given \(F = 5\ N\) and \(m = 10\ kg\), we substitute into \(a=\frac{F}{m}\). So, \(a=\frac{5\ N}{10\ kg}\).
\(a = 0.5\ m/s^{2}\).

• Answer: \(0.5\ m/s^{2}\)

1. For the fourth - type problem (Given a force of 88 N and an acceleration of 4 m/s², what is the mass?):

• Explanation:
• Step 1: Rearrange Newton's second - law formula

From \(F = ma\), we solve for \(m\) using \(m=\frac{F}{a}\).

• Step 2: Substitute the given values

Given \(F = 88\ N\) and \(a = 4\ m/s^{2}\), we substitute into \(m=\frac{F}{a}\). So, \(m=\frac{88\ N}{4\ m/s^{2}}\).
\(m = 22\ kg\).

• Answer: \(22\ kg\)

Answer:

1. For the first - type problem (How much force is required to accelerate a 2 kg mass at 3 m/s²?):

• Explanation:
• Step 1: Recall Newton's second - law formula

The formula for Newton's second law is \(F = ma\), where \(F\) is the force, \(m\) is the mass, and \(a\) is the acceleration.

• Step 2: Substitute the given values

Given \(m = 2\ kg\) and \(a=3\ m/s^{2}\), we substitute these values into the formula \(F = ma\). So, \(F=2\ kg\times3\ m/s^{2}\).
\(F = 6\ N\).

• Answer: \(6\ N\)

1. For the second - type problem (Given a force of 100 N and an acceleration of 10 m/s², what is the mass?):

• Explanation:
• Step 1: Rearrange Newton's second - law formula

From \(F = ma\), we can solve for \(m\) by the formula \(m=\frac{F}{a}\).

• Step 2: Substitute the given values

Given \(F = 100\ N\) and \(a = 10\ m/s^{2}\), we substitute into \(m=\frac{F}{a}\). So, \(m=\frac{100\ N}{10\ m/s^{2}}\).
\(m = 10\ kg\).

• Answer: \(10\ kg\)

1. For the third - type problem (What is the acceleration of a 10 kg mass pushed by a 5 N force?):

• Explanation:
• Step 1: Rearrange Newton's second - law formula

From \(F = ma\), we can solve for \(a\) by the formula \(a=\frac{F}{m}\).

• Step 2: Substitute the given values

Given \(F = 5\ N\) and \(m = 10\ kg\), we substitute into \(a=\frac{F}{m}\). So, \(a=\frac{5\ N}{10\ kg}\).
\(a = 0.5\ m/s^{2}\).

• Answer: \(0.5\ m/s^{2}\)

1. For the fourth - type problem (Given a force of 88 N and an acceleration of 4 m/s², what is the mass?):

• Explanation:
• Step 1: Rearrange Newton's second - law formula

From \(F = ma\), we solve for \(m\) using \(m=\frac{F}{a}\).

• Step 2: Substitute the given values

Given \(F = 88\ N\) and \(a = 4\ m/s^{2}\), we substitute into \(m=\frac{F}{a}\). So, \(m=\frac{88\ N}{4\ m/s^{2}}\).
\(m = 22\ kg\).

• Answer: \(22\ kg\)