Question

What is the force required to accelerate a 5 kg object from 2 m/s to 5 m/s in 2 seconds?

Answer 1

To find the force required to accelerate an object, we can use Newton's second law of motion, which states that:

\[
F = ma
\]

where \( F \) is the force, \( m \) is the mass of the object, and \( a \) is the acceleration.

1. **Find the acceleration (\( a \))**:
We can calculate the acceleration using the formula:

\[
a = \frac{\Delta v}{\Delta t}
\]

where \( \Delta v \) is the change in velocity and \( \Delta t \) is the change in time.

Given:
- Initial velocity \( v_i = 2 \, \text{m/s} \)
- Final velocity \( v_f = 5 \, \text{m/s} \)
- Time \( \Delta t = 2 \, \text{s} \)

Now, calculate the change in velocity (\( \Delta v \)):

\[
\Delta v = v_f - v_i = 5 \, \text{m/s} - 2 \, \text{m/s} = 3 \, \text{m/s}
\]

Now, calculate the acceleration:

\[
a = \frac{3 \, \text{m/s}}{2 \, \text{s}} = 1.5 \, \text{m/s}^2
\]

2. **Calculate the force (\( F \))**:
Now that we have the acceleration, we can find the force using the mass of the object:

Given:
- Mass \( m = 5 \, \text{kg} \)

Now substitute these values into the formula:

\[
F = ma = 5 \, \text{kg} \times 1.5 \, \text{m/s}^2
\]

\[
F = 7.5 \, \text{N}
\]

Thus, the force required to accelerate the 5 kg object from 2 m/s to 5 m/s in 2 seconds is **7.5 N**.