To calculate the velocity of a body after a certain time period given an initial velocity and constant acceleration, we use the first equation of motion:
[tex]\[ v = u + at \][/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.
We are given:
- Initial velocity, [tex]\( u = 0 \; \text{m/s} \)[/tex]
- Acceleration, [tex]\( a = 40 \; \text{m/s}^2 \)[/tex]
- Time, [tex]\( t = 7 \; \text{s} \)[/tex]
Now, let's substitute these values into the equation of motion:
[tex]\[ v = 0 \; \text{m/s} + (40 \; \text{m/s}^2 \times 7 \; \text{s}) \][/tex]
Calculating inside the parentheses first:
[tex]\[ 40 \; \text{m/s}^2 \times 7 \; \text{s} = 280 \; \text{m/s} \][/tex]
Then:
[tex]\[ v = 0 \; \text{m/s} + 280 \; \text{m/s} \][/tex]
[tex]\[ v = 280 \; \text{m/s} \][/tex]
Thus, the velocity of the body after 7 seconds is [tex]\( 280 \; \text{m/s} \)[/tex].
Since none of the provided options match our result exactly—assuming there might be a typographical error in the provided choices—the correct answer, based on our calculations, should be:
[tex]\[ \boxed{280 \; \text{m/s}} \][/tex]
