Linear Kinematics displacement velocity and acceleration Contents Quandary

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 vi - initial velocity vf - final velocity a - acceleration t - time (m) (m/s) (m/s/s) (s) 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 TOC

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

Whiteboards: How Far 1|2|3|4 TOC

What distance does a train go if it slows from 32. 0 m/s to 5. 0 m/s in 135 seconds? 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 W

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= 12 m/s, vf = ? ? , a = 1. 2 m/s/s, t = 5. 0 s x = vit + 1/2 at 2 x =75 m, 75 m W

Another car with a velocity of 27 m/s stops in a distance of 36. 74 m. What was its acceleration? x = 36. 74 m, vi = 27 m/s, vf = 0, a = ? ? , t = ? ? vf 2 = vi 2 + 2 ax a =-9. 9211 m/s/s, -9. 9 m/s/s W

A ship slows from 18 m/s to 12 m/s over a distance of 312 m. What time did it take? x = 312 m, vi = 18 m/s, vf = 12 m/s, t = ? ? x = (vi + vf)t 2 t =20. 8 s, 21 s W

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 = 47. 3 m, vi = ? ? , vf = 0, a = -9. 5 m/s/s, t = ? ? vf 2 = vi 2 + 2 as vi =29. 9783255 m/s, 30. m/s W

A cart stops in a distance of 3. 81 m in a time of 4. 51 s. What was its initial velocity? x = 3. 81 m, vi = ? ? , vf = 0, t = 4. 51 s x = (vi + vf)t 2 vi =1. 68958 m/s, 1. 69 m/s W

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 = 450 m, vi = 23 m/s, vf = ? ? , a = 3. 5 m/s/s, t = ? ? x = vit + 1/2 at 2 (Oh Nooooooo!) OR - use vf 2 = vi 2 + 2 as - find vf, and use vf = vi + at t =10. 7585 s, 11 s W

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

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