quadratic equation quadratic equations, such as x = v i t + ½ a t 2 can be tricky to solve. 3...
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![Page 1: Quadratic Equation Quadratic equations, such as x = v i t + ½ a t 2 can be tricky to solve. 3 strategies 1.Factoring (doesn’t usually work well with physics)](https://reader036.vdocuments.us/reader036/viewer/2022082818/56649f165503460f94c2b73e/html5/thumbnails/1.jpg)
Quadratic Equation
Quadratic equations, such as x = vit + ½ a t2
can be tricky to solve.
3 strategies1. 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.
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Quadratic Equation Solution• First, put your equation into this form: 0 = at2 + bt + c
for example, x = vit + ½ at2 becomes
0 = ½ at2 +vit – x
so , a = ½ a b = vi
c = -x
Then, use this equation to solve for t
![Page 3: Quadratic Equation Quadratic equations, such as x = v i t + ½ a t 2 can be tricky to solve. 3 strategies 1.Factoring (doesn’t usually work well with physics)](https://reader036.vdocuments.us/reader036/viewer/2022082818/56649f165503460f94c2b73e/html5/thumbnails/3.jpg)
Quadratic Equation Solution – We doA 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 abovethe ground?
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Quadratic Equation Solution – We doA 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 abovethe ground?
0 = ½ at2 +vit – x
so , a = ½ a = ½ * - 9.8 m/s2 = -4.9 m/s b = vi
= 15 m/s
c = -x = -10 m
tt = 0.5 sec and 1 sec
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Plugging in Numbers • Sometimes, you can just plug in numbers into the equation to
find the solution.• Works best with multiple choice.
![Page 6: Quadratic Equation Quadratic equations, such as x = v i t + ½ a t 2 can be tricky to solve. 3 strategies 1.Factoring (doesn’t usually work well with physics)](https://reader036.vdocuments.us/reader036/viewer/2022082818/56649f165503460f94c2b73e/html5/thumbnails/6.jpg)
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 sB. 10.2 sC. 13.4 sD. 15.1 S
![Page 7: Quadratic Equation Quadratic equations, such as x = v i t + ½ a t 2 can be tricky to solve. 3 strategies 1.Factoring (doesn’t usually work well with physics)](https://reader036.vdocuments.us/reader036/viewer/2022082818/56649f165503460f94c2b73e/html5/thumbnails/7.jpg)
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 sB. 10.2 sC. 13.4 sD. 15.1 S
Use x = vit + ½ at2 for each car and compare x. At which
answer choice does the truck final reach the car?
![Page 8: Quadratic Equation Quadratic equations, such as x = v i t + ½ a t 2 can be tricky to solve. 3 strategies 1.Factoring (doesn’t usually work well with physics)](https://reader036.vdocuments.us/reader036/viewer/2022082818/56649f165503460f94c2b73e/html5/thumbnails/8.jpg)
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 sB. 10.2 sC. 13.4 sD. 15.1 S
Use x = vit + ½ at2 for each car and compare x. At which
answer choice does the truck final reach the car?
![Page 9: Quadratic Equation Quadratic equations, such as x = v i t + ½ a t 2 can be tricky to solve. 3 strategies 1.Factoring (doesn’t usually work well with physics)](https://reader036.vdocuments.us/reader036/viewer/2022082818/56649f165503460f94c2b73e/html5/thumbnails/9.jpg)
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/s2. Car 2 has an initial velocity of 15 m/s and an acceleration of 2 m/s2. At one time will car 2 overtake car one?
A. 1.2 secB. 2.5s
C. 3.4 s D. 4.2 s
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Exit ticket & Homework
Exit ticket: write facts about circular motion
Homework:Circular acceleration problemsReview problemsExtra credit: Write 3 challenging physics problems and solve them on another sheet of paper.
Upcoming: CFA Wed / Thur next week. Exam right after break.