An object has 75 joules of kinetic energy in a mass of 1.5 kilograms. What is the velocity of the object?
Okay, let’s say that this is our object. And we know it’s in motion, that it does have some velocity by virtue of the fact that it has a nonzero kinetic energy. Let’s say our object is headed this way with some velocity, we’ll call that 𝑉, that we want to solve for. We’re told the mass of this object as well as its kinetic energy. And we can relate mass, kinetic energy, and velocity of the object through an equation for the kinetic energy of an object. The equation we can recall says that an object’s kinetic energy is equal to one-half its mass times its velocity squared.
And now, in our case, it’s not the object’s kinetic energy we want to solve for. After all, we’ve been given that value in the problem statement. It’s the velocity of the object 𝑉. To do that, we can rearrange this equation algebraically. As a first step, let’s multiply both sides by two divided by this object’s mass. Doing this cancels out the one-half factor, as well as the factor of 𝑚 on the right-hand side. And then if we take the square root of both sides of this equation, we see that that square root sign cancels out with the square of our velocity.
And we see that the velocity we want to solve for is equal to the square root of two times our object’s kinetic energy divided by its mass. Since we’re given the kinetic energy, as well as object mass in the problem statement, we can substitute in those values now. The velocity of this object is the square root of two times 75 joules divided by 1.5 kilograms. When we calculate this value, we’ll find it’s 10 metres per second. That’s velocity of this object given its kinetic energy and its mass.