Describing Motion free fall position from acceleration §2.5–2.6

Free Fall gravity alone

Free Fall Constant acceleration g = –9.8 m/s 2 down

Example Problem You launch a water balloon vertically from the top of a tall building as shown. Neglect air resistance. 1.The speed of the balloon at B compared to D is A. HigherB. LowerC. The sameD. Cannot tell 2.The speed of the balloon at A compared to E is A. HigherB. LowerC. The sameD. Cannot tell 3.The speed of the balloon at F compared to A is A. HigherB. LowerC. The sameD. Cannot tell 4.The time required to travel A  C compared to travel C  E is A. LongerB. ShorterC. The sameD. Cannot tell D E F A B C

Example Problem You launch a water balloon vertically from the top of a tall building as shown. Neglect air resistance. 5.Find the initial velocity of the balloon. 6.Find its total time in the air. 7.Find its velocity when it hits the ground. H D

Integrating Acceleration the most general case

Find Velocity from Acceleration General case: acceleration is derivative of velocity wrt time dv/dt. So, velocity is the integral of acceleration over time. a = dv/dt dv = a dt ∫dv = ∫a dt v = ∫a dt + v 0 You need to know the initial velocity!

Find Position from Velocity Velocity is derivative of position wrt time dx/dt. Position is the integral of velocity over time. v = dx/dt dx = v dt ∫dx = ∫v dt x = ∫v dt + x 0 You need to know the initial position!

Find Position from Acceleration Integrate twice Need to know v 0 and x 0