Answer :
Sure, let's solve the problem step-by-step:
### Problem Statement:
A force of 10 N acts on a body of mass 2 kg. If the body was initially at rest, calculate the velocity acquired by it in 5 seconds.
### Detailed Solution:
1. Identify the given values:
- Force (F) = 10 Newtons (N)
- Mass (m) = 2 kilograms (kg)
- Initial velocity (u) = 0 meters per second (m/s) (since the body is initially at rest)
- Time (t) = 5 seconds (s)
2. Use Newton's second law of motion:
Newton's second law states that the force (F) acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a):
[tex]\[ F = m \cdot a \][/tex]
Rearranging the formula to solve for acceleration (a):
[tex]\[ a = \frac{F}{m} \][/tex]
Plugging in the given values:
[tex]\[ a = \frac{10 \, \text{N}}{2 \, \text{kg}} = 5 \, \text{m/s}^2 \][/tex]
Therefore, the acceleration (a) of the body is [tex]\( 5 \, \text{m/s}^2 \)[/tex].
3. Calculate the final velocity:
We can use the first equation of motion to find the final velocity (v). The first equation of motion is:
[tex]\[ v = u + a \cdot t \][/tex]
Where:
- [tex]\( v \)[/tex] is the final velocity,
- [tex]\( u \)[/tex] is the initial velocity,
- [tex]\( a \)[/tex] is the acceleration,
- [tex]\( t \)[/tex] is the time.
Substituting the known values, we get:
[tex]\[ v = 0 \, \text{m/s} + 5 \, \text{m/s}^2 \cdot 5 \, \text{s} \][/tex]
[tex]\[ v = 25 \, \text{m/s} \][/tex]
### Final Answer:
The velocity acquired by the body after 5 seconds is [tex]\( 25 \, \text{m/s} \)[/tex].
### Problem Statement:
A force of 10 N acts on a body of mass 2 kg. If the body was initially at rest, calculate the velocity acquired by it in 5 seconds.
### Detailed Solution:
1. Identify the given values:
- Force (F) = 10 Newtons (N)
- Mass (m) = 2 kilograms (kg)
- Initial velocity (u) = 0 meters per second (m/s) (since the body is initially at rest)
- Time (t) = 5 seconds (s)
2. Use Newton's second law of motion:
Newton's second law states that the force (F) acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a):
[tex]\[ F = m \cdot a \][/tex]
Rearranging the formula to solve for acceleration (a):
[tex]\[ a = \frac{F}{m} \][/tex]
Plugging in the given values:
[tex]\[ a = \frac{10 \, \text{N}}{2 \, \text{kg}} = 5 \, \text{m/s}^2 \][/tex]
Therefore, the acceleration (a) of the body is [tex]\( 5 \, \text{m/s}^2 \)[/tex].
3. Calculate the final velocity:
We can use the first equation of motion to find the final velocity (v). The first equation of motion is:
[tex]\[ v = u + a \cdot t \][/tex]
Where:
- [tex]\( v \)[/tex] is the final velocity,
- [tex]\( u \)[/tex] is the initial velocity,
- [tex]\( a \)[/tex] is the acceleration,
- [tex]\( t \)[/tex] is the time.
Substituting the known values, we get:
[tex]\[ v = 0 \, \text{m/s} + 5 \, \text{m/s}^2 \cdot 5 \, \text{s} \][/tex]
[tex]\[ v = 25 \, \text{m/s} \][/tex]
### Final Answer:
The velocity acquired by the body after 5 seconds is [tex]\( 25 \, \text{m/s} \)[/tex].
