Article: To get an object's instantaneous velocity, first we have to have an equation that tells us its position (in terms of displacement) at a certain point in time. This means the equation must have the variable s on one side by itself and t on the other (but not necessarily by itself), like this:s = -1.5t2 + 10t + 4 In this equation, the variables are: Displacement = s . The distance the object has traveled from its starting position. For example, if an object goes 10 meters forward and 7 meters backward, its total displacement is 10 - 7 = 3 meters (not 10 + 7 = 17 meters). Time = t . Self explanatory. Typically measured in seconds. The derivative of an equation is just a different equation that tells you its slope at any given point in time. To find the derivative of your displacement formula, differentiate the function with this general rule for finding derivatives: If y = a*xn, Derivative = a*n*xn-1.This rule is applied to every term on the "t" side of the equation. In other words, start by going through the "t" side of your equation from left to right. Every time you reach a "t", subtract 1 from the exponent and multiply the entire term by the original exponent. Any constant terms (terms which don't contain "t") will disappear because they be multiplied by 0. This process isn't actually as hard as it sounds let's derive the equation in the step above as an example:s = -1.5t2 + 10t + 4(2)-1.5t(2-1) + (1)10t1 - 1 + (0)4t0-3t1 + 10t0-3t + 10 " To show that our new equation is a derivative of the first one, we replace "s" with the notation "ds/dt". Technically, this notation means "the derivative of s with respect to t." A simpler way to think of this is just that ds/dt is just the slope of any given point in the first equation. For example, to find the slope of the line made by s = -1.5t2 + 10t + 4 at t = 5, we would just plug "5" into t in its derivative. In our running example, our finished equation should now look like this:ds/dt = -3t + 10 Now that you have your derivative equation, finding the instantaneous velocity at any point in time is easy. All you need to do is pick a value for t and plug it into your derivative equation. For example, if we want to find the instantaneous velocity at t = 5, we would just substitute "5" for t in the derivative ds/dt = -3 + 10. Then, we'd just solve the equation like this:ds/dt = -3t + 10ds/dt = -3(5) + 10ds/dt = -15 + 10 = -5 meters/second Note that we use the label "meters/second" above. Since we're dealing with displacement in terms of meters and time in terms of seconds and velocity in general is just displacement over time, this label is appropriate.
Question: What is a summary of what this article is about?
Start with an equation for velocity in terms of displacement. Take the equation's derivative. Replace "s" with "ds/dt. Plug in a t value for your new equation to find instantaneous velocity.
Article: Numb or tingling lips could be related to a mild allergic reaction, especially when accompanied by itching, swelling, or an upset stomach. Try taking an over the counter allergy medication to manage numb or tingling lips and any accompanying symptoms. Note the food and drinks you consumed prior to the onset of your symptoms. Try to identify and eliminate the possible allergen from your diet. If you used a lip balm or similar product before experiencing numbness, stop using it. In severe food allergies, numbness and tingling can precede anaphylaxis, which is a life-threatening allergic response that requires immediate medical care. Call your local emergency services and use an autoinjector such as an Epi-Pen if you have one. If swelling accompanies your numbness, apply an ice pack to the affected area for 10 to 15 minutes. Swelling and numbness could result from an insect bite, a bump or other minor trauma, or allergies. Swelling could put too much pressure on facial nerves, which can cause numbness. You can also take an anti-inflammatory medication to help decrease swelling. If no swelling is present, avoid using a cold compress. The issue could be related to a lack of blood flow to your lips, and applying a warm compress can help increase blood flow. Decreased blood flow could be a simple reaction to cold temperatures, or could indicate an underlying issue, such as Raynaud's disease. If you experience additional symptoms, such as numbness in your extremities, contact your doctor. In addition to applying a warm compress, you could try massaging your lips to warm them and increase blood flow. Try moving your mouth and lips around and exhaling air between your lips to vibrate them. Wash your hands before and after massaging your lips. Numbness and tingling can occur just before a cold sore develops. If you suspect lip numbness might be due to a cold sore, apply an over the counter medicated ointment or talk to your doctor about a prescription antiviral pill. You could also try a homeopathic remedy such holding a slice of garlic over a cold sore for 10 to 15 minutes. However, even home remedies should be discussed with your doctor before use.
Question: What is a summary of what this article is about?
Take an antihistamine. Apply a cold compress to reduce swelling. Apply a warm compress if no swelling is present. Massage or wiggle the affected area. Use a medication to minimize a cold sore.
Article: Take your scooter to where the ground is wide and flat. Ride your scooter at a comfortable speed and when you feel ready, bend your knees and jump into the air. As you jump, pull the handlebars upward to draw the scooter deck up with you. Keep bending your knees as you land back on the ground and push the handlebars downward slightly. You don't need any ramps or hills to do a bunny hop. Mastering the bunny hop will help you prepare to learn more complex tricks. Put 1 foot on the back of your scooter deck and then kick off with your other foot. Gently lift the handlebars up so that the front wheel is airborne while keeping your other foot off the scooter deck and just above the ground. Use your hands to steer the scooter and swing your foot that's not on the deck to help keep yourself balanced. A manual is a great way to practice your balance and to learn a transition to use between different tricks. Ride your scooter forward and then place 1 foot down on the brake. Position your other foot so that it rests on the deck just in front of the brake. Pull the handlebars up to lift the front wheel and then bounce on the brake so that your scooter jumps slightly with only the back wheel touching the ground. The tire tap also make a good transition between more complicated tricks. Take your right hand off the handlebars and keep your left hand on. Then continue holding onto the handlebars with your left hand while you spin them as far as you comfortably can. When you can't spin the handlebars any further, bring your right hand under your left arm and grab the handlebars with your right hand. Remove your left hand from the handlebars and then complete the rotation with your right hand. Once you have rotated the handlebars by 360, return your left hand to the handlebars. You can start with either your left or right hand, as long as you complete the barspin with your opposite hand. The basic process is the same. When you first start, practice barspins while you are stationary by standing with 1 foot on the brake and lifting the front of the scooter off the ground. If you want to perform a barspin while you're riding, do a bunny hop as high as you can and complete the barspin while you're in the air.
Question: What is a summary of what this article is about?
Do a bunny hop to prepare for more complex tricks. Do a manual to ride just on the back wheel of your scooter. Try a tire tap to bounce on the back of your scooter. Perform a barspin to learn the basic maneuver for handlebar tricks.