An 8.0-gram bullet has a speed of 800 meters per second. What is its kinetic energy? What is its kinetic energy if the speed is halved?
We’re told the mass of the bullet, 8.0 grams, which we’ll refer to as 𝑚. We’re also told its speed of 800 meters per second; we’ll refer to that as 𝑣. In part one of the problem, we wanna solve for the kinetic energy of the bullet with this initial information.
Let’s begin our solution by recalling the equation for kinetic energy. The kinetic energy KE of an object is equal to half its mass times its speed squared. In our case, we know the mass, 8.0 grams, and the speed, 800 meters per second.
Before we plug these values in, we’ll want to convert the mass to a value in kilograms. Because 1000 grams is equal to one kilogram, the mass of 8.0 grams is equal to 8.0 times 10 to the negative third kilograms. Using that value for our mass and 800 meters per second for our speed, the kinetic energy of the bullet is 2.6 kilojoules. We use two significant figures in our answer because we were given two significant figures for the mass of the bullet.
In part two, we’re asked to solve for the kinetic energy of the bullet if its speed were cut in half, in other words if 800 meters per second were changed to 400 meters per second; we’ll call this value KE sub one-half. When we compute this value, we find an answer of 640 joules. We see that this value is less than half the initial kinetic energy. That’s because, in the equation for kinetic energy, the speed is squared.