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 Honors option Serve two hours a week in the helproom BPS 1248 must score 3 5 and above in all midterms PHY 231 PHYSICS 231 Lecture 3 Motion in 1 D part II PHY 231 2 Previously VECTORS Displacement Average Velocity Instantaneous velocity Average acceleration l Instantaneous acceleration SCALARS Distance Average speed Instantaneous speed MOTION DIAGRAMS PHY 231 3 Speed versus velocity A car travels from East Lansing to Okemos 3 km The trip takes 10 minutes 1 6 hour He then turns around and travels back It takes him 20 minutes 1 3 hour What was his average speed and average velocity over The whole trip a Average speed 13 5 km h Average velocity 12 km h b Average speed 12 km h Average velocity 0 km h c Average A speed d 13 5 13 5 km h k h Average A velocity l it 0 k km h h d Average speed 0 km h Average velocity 13 5 km h e Don t know Average velocity displacement time xf xi t Average speed speed distance time distance time Hence 6 1 6 1 3 12 Note xf xi PHY 231 4 PHY 231 5 PHY 231 6 Constant acceleration v t v0 at Velocity at t t equals equals Velocity at t 0 Plus the gain in velocity per second Multiplied by the time span every ry ssecond con th the velocity oc ty increases ncr as s With a m s PHY 231 7 Constant acceleration II x t xo v t xo v0 vt 2 t xo vot at 1 2 2 St t position Start iti plus l average velocity l it multiplied lti li d b by ti time Substitute v 0 vt v 2 Substitute PHY 231 v t v0 at 8 Constant Acceleration v V t is a straight line The area under the line in time interval t is v0 vt v0 vt x t 0 2 2 v t v0 t 0 The average velocity in defined as Hence Hence v 0 vt v 2 PHY 231 t t x v t 9 Review of Velocity PHY 231 10 Review of Acceleration PHY 231 11 Derivation v v0 t a v v0 v v0 v v x x0 v t 2 a 2a 2 2 0 v v 2a x x0 2 2 0 PHY 231 12 Important things Constant motion x t x0 x m v m s t v t 0 v t 0 Constant velocity x m x t x0 v0t t v m s v t v0 at v t v t a m s2 a t 0 t t v m s v t v 0 t a m s2 Constant acceleration x t x0 v0t at 2 x m a m s2 a t 0 PHY 231 t t a t a a t a0 t 13 x v a example 0 time Draw v vs t and a vs t PHY 231 14 Free fall 5 kg A B 1 kg 100 m x t xo vo t at 1 2 v t v0 at 2 a is the the acceleration felt due to gravitation commonly called g 9 8 m s2 Why no mass dependence PHY 231 15 v m s t 1 v 2 2 0 0 T s Q 1 2 1 What is the distance covered in 1 second 2 What is the area indicated by The area under the v t curve is equal to the displacement of the object PHY 231 a b c d 1 1 2 2 1 2 1 2 16 v m s t 1 v 2 2 0 0 T s Q 1 2 1 What is the distance covered in 1 second 2 What is the area indicated by The area under the v t curve is equal to the displacement of the object PHY 231 a b c d 1 1 2 2 1 2 1 2 17 a m s2 2 0 1 1 2 3 T s If the initial velocity at T 0 is 4 m s 1 What is the velocity at T 2 second 2 What is the area indicated by PHY 231 Q 1 2 a b c d 5 7 1 3 1 3 1 3 18 Kinematics in sports PHY 231 19 100 m dash what is the best strategy After long training Ben Lewis can accelerate with a 3 00 m s2 over a distance of 20 0 m Over the remaining 80 0 m h 80 0 he can maintain i t i thi this ttop speed d A After how many seconds Ben reaches his top speed B What is his speed p at that time C In how much time does he cross the finish line A 20 0 m 1 2 3 00 t2 t 3 65 s v B v t 3 65 3 00 t 10 95 m s C last 80 m t 80 10 95 7 30 s total time 3 65 7 30 10 95 s PHY 231 t 20 After a lot of training Ben manages to accelerate the first 3 65 s with a 4 00 m s2 After reaching his top speed he cannot maintain it however and d slowly l l d de accelerates l t a 0 4 0 4 m s 2 Did his hi ttotal t l time ti improve over 100 m A What distance does Ben cover while accelerating g B What is his speed at that time C How long does is take to cover to remaining distance and what is his total time v A x 1 2 4 00 3 652 26 6 m B v t 3 65 s 4 00 3 65 14 6 m s C 100 26 6 14 6 t 1 2 0 4 t2 t2 73 t 372 0 so t 5 51 or t 67 5 totall time i 3 3 65 5 51 9 16 65 5 51 9 16 PHY 231 t 21
View Full Document
Unlocking...