Let's solve this problem step by step using Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration [tex]\(F = ma\)[/tex].
1. Initial Condition:
- The given force [tex]\(F\)[/tex] is 20 N.
- The mass [tex]\(m\)[/tex] of the block is 4 kg.
To find the initial acceleration, we rearrange Newton's second law to solve for acceleration [tex]\(a\)[/tex]:
[tex]\[
a = \frac{F}{m}
\][/tex]
2. Calculate the Initial Acceleration:
[tex]\[
a = \frac{20\, \text{N}}{4\, \text{kg}} = 5\, \text{m/s}^2
\][/tex]
So, the initial acceleration is [tex]\(5 \, \text{m/s}^2\)[/tex].
3. When the Force is Doubled:
- The new force [tex]\(F'\)[/tex] is [tex]\(2 \times 20 \, \text{N} = 40 \, \text{N}\)[/tex].
Using Newton's second law again to find the new acceleration [tex]\(a'\)[/tex]:
[tex]\[
a' = \frac{F'}{m}
\][/tex]
4. Calculate the New Acceleration:
[tex]\[
a' = \frac{40\, \text{N}}{4\, \text{kg}} = 10\, \text{m/s}^2
\][/tex]
So, the new acceleration when the force is doubled is [tex]\(10 \, \text{m/s}^2\)[/tex].
In conclusion, the initial acceleration of the block is [tex]\(5 \, \text{m/s}^2\)[/tex] and the acceleration when the force is doubled is [tex]\(10 \, \text{m/s}^2\)[/tex].
