Quadratic Equation Quadratic equations such as x vit
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Quadratic Equation Quadratic equations, such as x = vit + ½ a t 2 can be tricky to solve. 3 strategies 1. Factoring (doesn’t usually work well with physics) 2. Quadratic Equation solution (always works, but you need to memorize) 3. Trial & Error / Plugging in values (can be useful for multiple choice) We will talk about #2 and #3.
Quadratic Equation Solution • First, put your equation into this form: 0 = at 2 + bt + c for example, x = vit + ½ at 2 becomes 0 = ½ at 2 +vit – x so , a = ½ a b = vi c = -x Then, use this equation to solve for t
Quadratic Equation Solution – We do A ball is launched upward with a speed of 15 m/s from an intial height of 5 m. What are the two approximate times that the object will be located at the height of 10 m above the ground?
Quadratic Equation Solution – We do A ball is launched upward with a speed of 15 m/s from an intial height of 5 m. What are the two approximate times that the object will be located at the height of 10 m above the ground? 0 = ½ at 2 +vit – x so , a = ½ * - 9. 8 m/s 2 = -4. 9 m/s b = vi = 15 m/s c = -x = -10 m tt = 0. 5 sec and 1 sec
Plugging in Numbers • Sometimes, you can just plug in numbers into the equation to find the solution. • Works best with multiple choice.
Plugging in Numbers • Sometimes, you can just plug in numbers into the equation to find the solution. • Works best with multiple choice. Example – WE DO • A car and truck start from the same position. The car has a constant velocity of 20 m/s. The truck has an initial velocity of zero, but accelerates 3 m/s. At approximately what time does the truck overtake the car? A. 6. 6 s B. 10. 2 s C. 13. 4 s D. 15. 1 S
Plugging in Numbers • Sometimes, you can just plug in numbers into the equation to find the solution. • Works best with multiple choice. Example – WE DO • A car and truck start from the same position. The car has a constant velocity of 20 m/s. The truck has an initial velocity of zero, but accelerates 3 m/s. At approximately what time does the truck overtake the car? A. 6. 6 s B. 10. 2 s C. 13. 4 s D. 15. 1 S Use x = vit + ½ at 2 for each car and compare x. At which answer choice does the truck final reach the car?
Plugging in Numbers • Sometimes, you can just plug in numbers into the equation to find the solution. • Works best with multiple choice. Example – WE DO • A car and truck start from the same position. The car has a constant velocity of 20 m/s. The truck has an initial velocity of zero, but accelerates 3 m/s. At approximately what time does the truck overtake the car? A. 6. 6 s B. 10. 2 s C. 13. 4 s D. 15. 1 S Use x = vit + ½ at 2 for each car and compare x. At which answer choice does the truck final reach the car?
Quadratic Equation – You do • A ball is dropped from 15 ft. At what time will the ball be 5 ft from the ground? • Car 1 and Car 2 start at the same position. Car 1 has an initial velocity of 10 m/s and an acceleration of 5 m/s 2. Car 2 has an initial velocity of 15 m/s and an acceleration of 2 m/s 2. At one time will car 2 overtake car one? A. 1. 2 sec B. 2. 5 s C. 3. 4 s D. 4. 2 s
Exit ticket & Homework Exit ticket: write facts about circular motion Homework: Circular acceleration problems Review problems Extra credit: Write 3 challenging physics problems and solve them on another sheet of paper. Upcoming: CFA Wed / Thur next week. Exam right after break.
