An object of mass [tex]16 \, \text{kg}[/tex] is moving with an acceleration of [tex]3 \, \text{m/s}^2[/tex]. Calculate the applied force. If the same force is applied to an object of mass [tex]24 \, \text{kg}[/tex], what will be the acceleration?

Given:
[tex]\[ m_1 = 16 \, \text{kg} \][/tex]



Answer :

Of course! Let's go through the solution step by step.

### Step 1: Calculate the Applied Force

We are given:
- Mass, [tex]\( m_1 = 16 \)[/tex] kg
- Acceleration, [tex]\( a_1 = 3 \)[/tex] m/s²

We need to calculate the applied force using Newton's second law of motion, which is given by:
[tex]\[ F = m \times a \][/tex]

Substituting the known values:
[tex]\[ F = 16 \, \text{kg} \times 3 \, \text{m/s}^2 \][/tex]
[tex]\[ F = 48 \, \text{N} \][/tex]

So, the applied force is [tex]\( 48 \)[/tex] Newtons (N).

### Step 2: Calculate the Acceleration for the Second Object

We are now given:
- The applied force, [tex]\( F = 48 \)[/tex] N (which we just calculated)
- The mass of the second object, [tex]\( m_2 = 24 \)[/tex] kg

We need to calculate the acceleration using the same applied force on the new mass. Again, using Newton's second law:
[tex]\[ F = m \times a \][/tex]

Rearranging for acceleration [tex]\( a \)[/tex]:
[tex]\[ a = \frac{F}{m} \][/tex]

Substituting the known values:
[tex]\[ a_2 = \frac{48 \, \text{N}}{24 \, \text{kg}} \][/tex]
[tex]\[ a_2 = 2 \, \text{m/s}^2 \][/tex]

So, the acceleration of the second object with mass [tex]\( 24 \)[/tex] kg under the same applied force is [tex]\( 2 \)[/tex] m/s².

### Summary
- The applied force on the initial object is [tex]\( 48 \)[/tex] N.
- When the same force is applied to a second object of mass [tex]\( 24 \)[/tex] kg, the resulting acceleration is [tex]\( 2 \)[/tex] m/s².