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If a body moves at [tex]120 \, \text{m/s}[/tex] starting from [tex]0 \, \text{m/s}[/tex] at [tex]t=0[/tex] and accelerates at a constant rate of [tex]40 \, \text{m/s}^2[/tex], calculate its velocity at 7 seconds.

A. [tex]400 \, \text{m/s}[/tex]
B. [tex]45 \, \text{m/s}[/tex]
C. [tex]450 \, \text{m/s}[/tex]
D. [tex]300 \, \text{m/s}[/tex]



Answer :

GinnyAnswer
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]

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