**– Acceleration.**

**– Velocity.**

**– Speed.**

**– All of the above.**

**Choose the correct option from the given choices.**

The main objective of this question is to **choose** the c**orrect option** from the** given options** when you apply **double** **force** on an **object**.

This question uses the concept of **Newton’s second law** of **motion**. Newton’s second law states that **force** is equal to the product of mass and acceleration. It is mathematically represented as:

\[ \space F \space = \space m a \]

**Where** $ FÂ $ is **force**, **mass** is $ m $ and **acceleration** is $Â a $.

## Expert Answer

We have to choose the **correct option** from the given options when the** force applied** to the **object** is **doubled**.

We know from **Newton’s second law** that force is equal to the **product** of **mass** and **acceleration**.

**Thus**:

\[ \space F \space = \space m a \]

Given that the **force is doubled**, so:

\[ \space 2 \space \times \space F \space = \space 2 \space \times \space m a \]

\[ \space 2F \space = \space m \space ( 2 a ) \]

Thus, we the **force is double**, we have:

\[ \space 2F \space = \space m \space ( 2 a ) \]

## Numerical Answer

We know that when the **force is doubled**, we have:

\[ \space 2F \space = \space m \space ( 2 a ) \]

Thus force is **directly proportional** to the** acceleration magnitude, **so the **correct option** from the given options is **acceleration**.

## Example

Find the **net force** of an **object** which has a **mass** ofÂ $ 100 kg \space and 150kg $ while the **acceleration** isÂ $ 5 \frac{m}{s^2} $.

**Given that**:

\[ \space accelerationÂ \space = \spaceÂ 5 \frac{m}{s^2} \]

\[ \space mass \space = \space 100 kg \]

We have to **find** the **net force**. From Newton’s second law of motion, we know that **force** is equal to the **product** of **mass** and **acceleration**. It is **mathematically** represented as:

\[ \space F \space = \space m a \]

**Where** $ FÂ $ is force, **mass** is $ m $ and **acceleration** is $Â a $.

By **putting** the **values**, we get:

\[ \space F \space = \space 100 \space \times \space 5\]

\[ \space F \space = \space 500 \space N \]

**Now** for the **mass** of $ 150 kg $. **Given that**:

\[ \space accelerationÂ \space = \spaceÂ 5 \frac{m}{s^2} \]

\[ \space mass \space = \space 100 kg \]

We have to **find** the **net force**. From Newton’s second law of motion, we know that **force** is equal to the **product** of **mass** and **acceleration**. It is **mathematically** represented as:

\[ \space F \space = \space m a \]

**Where** $ FÂ $ is force, **mass** is $ m $ and **acceleration** is $Â a $.

By **putting** the **values**, we get:

\[ \space F \space = \space 150 \space \times \space 5\]

\[ \space F \space = \space 750 \space N \]

Thus, the net force for $ 100 kg $ is $ 500 N $, and for $ 150 kg $ the net force is $ 750Â N $.