Physics 231 non calculus introductory physics I Section 003 http www pa msu edu people yuan classes htm http www pa msu edu people yuan classes htm Helproom p BPS 1248 hours Mon 3pm 7pm Tue 9am 11 30am 3pm 7pm Wed 9am 12pm 1pm 7pm Thur 1pm 6pm Fri 9am 12pm 1pm 6pm PHY 231 PHYSICS 231 Lecture 2 Motion in 1 dimension part I PHY 231 2 Galileo 1564 1642 Whatt mathematical Wh th ti l forces f govern accelerated motion A wooden and stone sphere are dropped from the tower of pisa Which one reaches the earth first Answer same time PHY 231 3 The inclined plane experiment Distance traveled goes with the square of time x t t2 Time measured with water PHY 231 4 Displacement t 1 X 30 t 0 X 0 X 30 X 45 Displacement Di l iis a vector and d thus h h has direction di i sign i Displacement is not equal to Distance X 30 t 1 t 0 X 0 X 30 PHY 231 X 45 5 Average Velocity Average velocity Displacement Time interval x x f xi v t t f ti t 0 t 2 t 1 t 0 t 1 t 2 X 0 X 0 X 30 X 45 Which object has the largest average velocity over 2 s a b c PHY 231 6 Graphically x m x x f xi v t t f ti slope t s The average velocity is the slope of the line connecting begin end end point in the x t graph Ignore what happens in between between PHY 231 7 Vectors and Scalars X 30 t 1 t 0 X 0 X 30 x x f xi 30 v t t f ti speed x t x f xi t f ti PHY 231 X 45 Average velocity vector 30 Average speed scalar 8 Instantaneous Velocity But officer my average speed d was only 25 miles per hour Sometimes we want to know the speed at one particular point in time time PHY 231 9 PHY 231 10 Instantaneous velocity x m x x f xi v t t f ti t s What is the Velocity at t 2 t 2 0 0 s Consider the average velocity for a very small time interval with t 2 0 t 2 0 s in the center PHY 231 11 Instantaneous velocity x m x t x v lim t 0 t t s PHY 231 12 Instantaneous velocity x m x t x v lim li t 0 t x v t tangent t t s v slope of the tangent to the x t curve at t 2 0 s Think about the sign PHY 231 13 Question x A B t x x f xi v t t f ti x v t tangent t Which object j had the largest g average g velocity y B Which object had the largest instantaneous velocity B PHY 231 14 x Acceleration A change in slope in the x t graph t v means a change in velocity Acceleration PHY 231 t 15 Acceleration v f vi t f ti Average acceleration Instantaneous acceleration v a lim t 0 t vv a t tangent PHY 231 16 Question v t 0 v 20 t 1 v 5 t What is the average acceleration between t 0 and t 1 A 15 B 15 15 PHY 231 C 0 D iinfinity fi it 17 Constant positive velocity PHY 231 18 Positive velocity and acceleration PHY 231 19 GALILEO A Question B C Which vv tt diagram matches which a a tt diagram PHY 231 20
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