– 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 correct 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 $ F $ is force, mass is $ m $ and acceleration is $ 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 of $ 100 kg \space and 150kg $ while the acceleration is $ 5 \frac{m}{s^2} $.
Given that:
\[ \space acceleration \space = \space 5 \frac{m}{s^2} \]
\[ \space mass \space = \space 100 kg \]
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 $ F $ is force, mass is $ m $ and acceleration is $ 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:
\[ \space acceleration \space = \space 5 \frac{m}{s^2} \]
\[ \space mass \space = \space 100 kg \]
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 $ F $ is force, mass is $ m $ and acceleration is $ 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 $ 750 N $.