1. Graphical Analysis of Linear Motion

2. A car travels along a road at a constant velocity of 10. m/s time (s) position (m) 0 0 1 10 2 20 3 30

3. slope = Δx/Δt ΔtΔt ΔxΔx = 20 m/2 s = 10 m/s velocity

4. position vs. time graph to find displacement: to find velocity: subtract values from graph find slope if straight line acceleration = 0

5. Displacement for 1 st 3 seconds: 30 m area under graph slope:0acceleration

6. v vs. t graph to find displacement: to find velocity: to find acceleration: find area read graph find slope

7. Object dropped from a tall building (use g = 10 m/s 2 ) time (s) position (m) 0 0 1 5 2 20 3 45 x = x 0 + v 0 t + ½ at 2 x 0 = 0; v 0 = 0

8. velocity @ 2 s: slope of tangent line slope = 20/1 = 20 m/s

9. time (s) velocity (m/s) 0 0 1 10 2 20 3 30 v = v 0 + at

10. acceleration @ 2 s:slope 10 m/s 2 displacement for 1 st 3 s:area Δx = 45 m

11. area:30 m/s= Δv

12. Graphs (vs. time) position velocityacceleration slope area

13. If acceleration is positive (constant); x 0 = 0; v 0 = 0 x = ½ at 2

14. To produce a straight-line graph: slope = ½ a also: t 2 vs. x, x vs. t, t vs. x

20. Graphs of x, v, a