Linear Kinematics - displacement, velocity and acceleration Contents: Quandary New formula Deriving the rest of the formulas How to solve these: suvat Whiteboards

A new formula: x = (vi + vf)t 2 x - displacement (m) vi - initial velocity (m/s) vf - final velocity (m/s) a - acceleration (m/s/s) t - time (s) x = (vi + vf)t 2 A car goes from 14 m/s to 26 m/s in 10. seconds. How far does it go in this time? x = (14 m/s + 26 m/s)(10. s) = 200 m = 2.0 x 102 m 2 A person starts from rest and goes 14.5 m in 3.75 s. What is their final velocity? 14.5 m = (0 + vf)(3.75 s), vf = 7.73333 = 7.73 m/s 2

Deriving: - 2 more nifty formulas!! vf = vi + at x = (vi + vf)t 2 From the first formula: t = (vf - vi) a Derive: vf2 = vi2 + 2ax x = vit + 1/2at2 when to use which one… x - displacement (m) vi - initial velocity (m/s) vf - final velocity (m/s) a - acceleration (m/s/s) t - time (s) Look at your blue formula sheets!!

Whiteboards: How Far 1 | 2 | 3 | 4

show all steps What distance does a train go if it slows from 32.0 m/s to 5.0 m/s in 135 seconds? X Vi Vf a t x = ?, vi = 32.0 m/s, vf = 5.0 m/s, t = 135 s x = (vi + vf)t 2 x =2497.5 m, 2500 m 2500 m

label knowns Another car with a velocity of 27 m/s stops in a distance of 36.74 m. What was its acceleration? X Vi Vf a t x = 36.74 m, vi = 27 m/s, vf = 0, a = ??, t = ?? vf2 = vi2 + 2ax a =-9.9211 m/s/s, -9.9 m/s/s -9.9 m/s/s

A car going 12 m/s accelerates at 1. 2 m/s/s for 5. 0 seconds A car going 12 m/s accelerates at 1.2 m/s/s for 5.0 seconds. What is its displacement during this time? X Vi Vf a t x = ?, vi= 12 m/s, vf = ??, a = 1.2 m/s/s, t = 5.0 s x = vit + 1/2at2 x =75 m, 75 m 75 m

show two step trick A cart stops in a distance of 13.8 m in a time of 4.51 s. What was its acceleration? X Vi Vf a t x = 13.8 m, vf = 0, t = 4.51 s, a = find vi first, then a vi = 6.1197 m/s a = -1.3569 m/s/s -1.36 m/s/s

show two step trick What time will it take a car going 23 m/s to start with, and accelerating at 3.5 m/s/s, to go 450 m? X Vi Vf a t x = 450 m, vi = 23 m/s, vf = ??, a = 3.5 m/s/s, t = ?? x = vit + 1/2at2 (Oh Nooooooo!) OR - use vf2 = vi2 + 2as - find vf, and use vf = vi + at t =10.7585 s, 11 s 11 s

A car’s brakes slow it at 9. 5 m/s/s. If it stops in 47 A car’s brakes slow it at 9.5 m/s/s. If it stops in 47.3 m, how fast was it going to start with? X Vi Vf a t x = 47.3 m, vi = ??, vf = 0, a = -9.5 m/s/s, t = ?? vf2 = vi2 + 2as vi =29.9783255 m/s, 30. m/s 30. m/s

A ship slows from 18 m/s to 12 m/s over a distance of 312 m A ship slows from 18 m/s to 12 m/s over a distance of 312 m. What time did it take? X Vi Vf a t x = 312 m, vi = 18 m/s, vf = 12 m/s, t = ?? x = (vi + vf)t 2 t =20.8 s, 21 s 21 s

Start Basic Problem Solving Is it Bigger than Your Mouth? Yes Cut it up a bit No Eat it Done

Start Basic Problem Solving Write down given quantities Are you done yet? No Apply any formula Yes Circle the answer