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A [tex][tex]$6.7 kg$[/tex][/tex] object moves with a velocity of [tex][tex]$8 m / s$[/tex][/tex]. What's its kinetic energy?

A. [tex][tex]$26.8 J$[/tex][/tex]
B. [tex][tex]$214.4 J$[/tex][/tex]
C. [tex][tex]$167.5 J$[/tex][/tex]
D. [tex][tex]$53.6 J$[/tex][/tex]


Sagot :

To find the kinetic energy of the object, we start by using the formula for kinetic energy:

[tex]\[ \text{Kinetic Energy} = \frac{1}{2} \times \text{mass} \times \text{velocity}^2 \][/tex]

We are given:
- Mass ([tex]\( m \)[/tex]) = 6.7 kg
- Velocity ([tex]\( v \)[/tex]) = 8 m/s

Substitute these values into the formula:

[tex]\[ \text{Kinetic Energy} = \frac{1}{2} \times 6.7 \times 8^2 \][/tex]

Calculate the velocity term first:

[tex]\[ 8^2 = 64 \][/tex]

Now, multiply that by the mass:

[tex]\[ 6.7 \times 64 = 428.8 \][/tex]

Finally, take half of the result to find the kinetic energy:

[tex]\[ \frac{1}{2} \times 428.8 = 214.4 \][/tex]

So, the kinetic energy is:

[tex]\[ 214.4 \text{ Joules} \][/tex]

The best answer is:
[tex]\[ \text{B. } 214.4 \text{ J} \][/tex]