Ch1: 1D Kinematics 1.Recall main points: position, displacement, velocity and acceleration (geometrically and algebraically) 2.Discuss Pre-lecture and Check Points 3.Examples of problems

1.1 Main Points Position x of point P in 1D: Axis, Origin, Direction Average velocity of P between times t1 and t2: Instantaneous Velocity of P at time t: Instantaneous acceleration of P at t:

1.1 Main Points Graphical relationship from x to v to a. Example start with a=cst a v x t t t -2m/s 2 Slope= 2 m/s Slope= -2 m/s t=5s A B C D , 3 and 4 62 and 3 Given a find v then x:

1.1 Main Points Algebraic relationship from x to v=velocity to a=acceleration. Start with x(t)=2t-1 Meaning of the coef. 2 and -1. They depend on t=0 and origin of axis In general for x=At+B: Second derivative /t: First derivative /time: At t=0: So that we define:

1.1 Main Points Motion with constant a: from a to x Graphical x, v, a Algebraic x, v, a

1.2 Discuss For the Displacement and Velocity curves shown on the left, which is the correct plot of acceleration vs. time?

1.2 Discuss Set up problem (always same way ): 1.Picture: Axes with origin and direction 2.Equations relevant to problem and specified for axis choice 3.Constraint Equations 4.Solution At t = 0 a ball, initially at rest, starts to roll down a ramp with constant acceleration. Suppose it moves 1 m between t = 0 sec and t = 1 sec. How far does it move between t = 1 sec and t = 2 sec ? CheckPoint 2:

1.3 problems Relative signs of v, a and relation to speed and slowing down or speeding up. Difference between the quantity and its magnitude.

Example. Throw an object up in the air. A. How high does it go above release point, given v o ? 1.3 problems

B. How long does it stay in the air, given v o ? Example. Throw an object up in the air, cont’d

Example. Two objects up in the air. Released same time, one from h at v o =0, the other from y=0 at v o After how long do they meet? 1.3 problems

Example. 1.3 problems

Ch 1: Assignments