To determine the velocity of a body after a given time when accelerated by a constant force, follow these steps:
1. Identify the given data:
- Mass ([tex]\( m \)[/tex]) of the body: [tex]\( 1 \, \text{kg} \)[/tex]
- Force ([tex]\( F \)[/tex]) applied: [tex]\( 2 \, \text{N} \)[/tex]
- Time ([tex]\( t \)[/tex]) of motion: [tex]\( 5.0 \, \text{s} \)[/tex]
2. Calculate the acceleration:
- According to Newton's second law of motion, force is the product of mass and acceleration:
[tex]\[
F = ma
\][/tex]
Solving for acceleration ([tex]\( a \)[/tex]):
[tex]\[
a = \frac{F}{m} = \frac{2 \, \text{N}}{1 \, \text{kg}} = 2 \, \text{m/s}^2
\][/tex]
3. Determine the initial velocity:
- Assuming the initial velocity ([tex]\( u \)[/tex]) is [tex]\( 0 \, \text{m/s} \)[/tex] (i.e., the body starts from rest).
4. Calculate the final velocity:
- Use the kinematic equation that relates initial velocity ([tex]\( u \)[/tex]), acceleration ([tex]\( a \)[/tex]), and time ([tex]\( t \)[/tex]) to the final velocity ([tex]\( v \)[/tex]):
[tex]\[
v = u + at
\][/tex]
Substituting in the known values:
[tex]\[
v = 0 \, \text{m/s} + (2 \, \text{m/s}^2 \times 5.0 \, \text{s}) = 10 \, \text{m/s}
\][/tex]
Therefore, the velocity of the body after [tex]\( 5.0 \)[/tex] seconds of motion is [tex]\( 10 \, \text{m/s} \)[/tex].
