In one sentence, describe what the following article is about: when acceleration is constant. If an object is accelerating at a constant rate, the formula for average velocity is simple:vav=vi+vf2{\displaystyle v_{av}={
rac {v_{i}+v_{f}}{2}}}. In this equation vi{\displaystyle v_{i}} is the initial velocity, and vf{\displaystyle v_{f}} is the final velocity. Remember, you can only use this equation if there is no change in acceleration. As a quick example, let's say a train accelerates at a constant rate from 30 m/s to 80 m/s. The average velocity of the train during this time is 30+802=55m/s{\displaystyle {
rac {30+80}{2}}=55m/s}. You can also find the velocity from the object's change in position and time. This works for any problem. Note that, unless the object is moving at a constant velocity, your answer will be the average velocity during the movement, not the specific velocity at a certain time. The formula for this problem is vav=xfxitfti{\displaystyle v_{av}={
rac {x_{f}-x_{i}}{t_{f}-t_{i}}}}, or "final position - initial position divided by final time - initial time." You can also write this as vav{\displaystyle v_{av}} = x / t, or "change in position over change in time." When measuring velocity, the only positions that matter are where the object started, and where the object ended up. This, along with which direction the object traveled, tells you the displacement, or change in position. The path the object took between these two points does not matter. Example 1: A car traveling due east starts at position x = 5 meters. After 8 seconds, the car is at position x = 41 meters. What was the car's displacement? The car was displaced by (41m - 5m) = 36 meters east. Example 2: A diver leaps 1 meter straight up off a diving board, then falls downward for 5 meters before hitting the water. What is the diver's displacement? The diver ended up 4 meters below the starting point, so her displacement is 4 meters downward, or -4 meters. (0 + 1 - 5 = -4). Even though the diver traveled six meters (one up, then five down), what matters is that the end point is four meters below the start point. How long did the object take to reach the end point? Many problems will tell you this directly. If it does not, subtract the start time from the end time to find out. Example 1 (cont.): The problem tells us that the car took 8 seconds to go from the start point to the end point, so this is the change in time. Example 2 (cont.): If the diver jumped at t = 7 seconds and hits the water at t = 8 seconds, the change in time = 8s - 7s = 1 second. In order to find the velocity of the moving object, you will need to divide the change in position by the change in time. Specify the direction moved, and you have the average velocity. Example 1 (cont.): The car changed its position by 36 meters over 8 seconds. vav=36m8s={\displaystyle v_{av}={
rac {36m}{8s}}=} 4.5 m/s east. Example 2 (cont): The diver changed her position by -4 meters over 1 second. vav=4m1s={\displaystyle v_{av}={
rac {-4m}{1s}}=} -4 m/s. (In one dimension, negative numbers are usually used to mean "down" or "left." You could say "4 m/s downward" instead.) Not all word problems involve movement back along one line. If the object turns at some point, you may need to draw a diagram and solve a geometry problem to find the distance. Example 3: A man jogs for 3 meters east, then make a 90 turn and travels 4 meters north. What is his displacement? Draw a diagram and connect the start point and end point with a straight line. This is the hypotenuse of a triangle, so solve for its length of this line using properties of right triangles. In this case, the displacement is 5 meters northeast. At some point, your math teacher may require you to find the exact direction traveled (the angle above the horizontal). You can do this by using geometry or by adding vectors.
Summary: Find average velocity Set up an equation with position and time instead. Find the distance between the start and end points. Calculate the change in time. Divide the total displacement by the total time. Solve problems in two dimensions.

Problem: Article: Sometimes in order to accomplish what feels like a monumental task, you have to start small. For now, just go and turn on the shower. Get the water nice and warm and think about how good it would feel to climb inside. You'll probably find it much easier to shower once you're actually in the bathroom and have everything all ready to go. The hardest part often lies in simply taking the first step. Remember, the only thing holding you back is lethargy. With that out of the way, nothing can stop you. At this point, it will probably feel silly to have gone to all that trouble just to shut off the water and put your clothes back on. Since you're already in position, and it requires just as much effort to get dressed again, you might as well go ahead and hop in the shower. When you're lounging comfortably on the couch, the list of things you need to do to successfully bathe can seem overwhelming. Instead of trying to focus on lots of details at once, move things along a little at a time. If you find that you lack the motivation to shower, it can be helpful to keep in mind what happens when you don't bathe regularly. Dirt, oil and dead cells can build up on your skin, making you feel grimy and uncomfortable. If you go too long, this can cause problems like itching, clogged pores and skin infections. After a while, you can start to smell, as well, which can be a source of social embarrassment. It can be bad for you to go too long without a bath or shower. Skin conditions like acne, dermatitis and chronic body odor can develop, making you look and feel unhealthy. There's no need to shower every day. In fact, dermatologists now believe that it's actually better for you to only shower a few times a week. This may make dealing with the task easier for you.
Summary:
Turn on the water. Once you've made it to the bathroom and got the shower running, strip down and see how you feel. Remind yourself why you need to shower.