Given that the kinetic energy of a moving bullet of mass one over 35 kilograms at a certain instant was 7,000 joules, determine its speed.
So the first thing we notice is that this problem is a kinetic energy problem. So the first thing we can do is remind ourselves of the kinetic energy formula, and that is that kinetic energy is equal to a half 𝑚𝑣 squared. And as with our question, when we have the kinetic energy in joules and the mass in kilograms, then we know that the velocity or speed is going to be in meters per second.
So what we’re gonna do now is put the values we’ve got from mass and our kinetic energy into the formula. So what we’re gonna get is 7,000 is equal to a half multiplied by one over 35 multiplied by 𝑣 squared. So therefore, we can say that 7,000 is gonna be equal to 𝑣 squared over 70. And we got that because a half multiplied by one over 35 is one over 70. So then we multiply this by 𝑣 squared; it gives us 𝑣 squared over 70. So then, what we do is multiply both sides of the equation by 70. And so what we’re gonna get is 490,000 equals 𝑣 squared. So then next, what we do is take the square root of both sides. So when we do that, we get 700 is equal to 𝑣.
But what you’ve noticed here is that we’ve disregarded the possible negative value, which is a result of the square root of 490,000. And the reason that we don’t have to consider that negative value is because we’re looking at speed. And speed is always positive because what it is is the magnitude of the velocity vector. So therefore, it will always be a positive result. So therefore, we can say that given the kinetic energy of a moving bullet of mass one over 35 kilograms at a certain instant is 7,000 joules, then its speed will be 700 meters per second.