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Races and Circular Motion Concept

                                       Races & Circular Motion
Concept:-

Linear RacesBeat by DistanceBeat by TimettABA, BTime is constant∴ Speed ∝ DistanceA beat B by distance d then A cover total distance D in t time while B cover (D - d) distance in t timettA, BA, BDistance is constant∴ Speed ∝ A beat B by time t. then A reaches end point in timet then B reaches end point intime t which is (t + t)Example: In a 1 km. race A beats B by 100 m. Find ratio of speeds of A & BSol:-Example: In a 1 km. race A beats B by 10 sec. Find ratio of speeds of A & BSol:-ttABA, B100 m A BDistane 1000 900 10 : 9Speed 10 : 9 Answer A BTime t (t + 10) Speed (t + 10) : t Answer

Example: In a 1 km. race A beats B by 50 m or 10 sec. What time does A take to completer the race.
Sol:-
A beats B by 50 m or 10 sec. So B will cover 50 m in 10 sec.
Speed of B = \(\frac{{50}}{{10}}\) = 5 m/sec
time taken by B to run 1 Km. = \(\frac{{1000}}{5}\) = 200 sec.
∴ time taken by A to run 1 km. = 200 – 10
= 190 sec                 Answer

Circular Motion (Race)ConceptBAAB

● When will first tim they meet ?
● When will they meet first time at starting point.
● How many times they will meet on the track.

BAAB2 m/sec5 m/sec210 m210 m2 m/sec5 m/sec● time for first time meeting(i). Answer● time taken by A to reachstarting point(ii) ∴ time to meet first time at the starting point = LCM(42, 105) = 210 Answer● Number of times they will meeton track = write their speed in simplest formso that there is no factor commonin them then subtract them to getnumber of times they will meet.⟹ 5 - 2 = 3 AnswerAnswer●(i) time for first time meeting = ●(ii) time taken by A to reach starting point time take by B to reach starting point = = 105 sec ∴ time to meet first time at the starting point = LCM(42, 105) = 210 Answer●(iii) Number of times they will meeton track = write their speed in simplest formso that there is no factor commonin them then add them to getnumber of times they will meet.⟹ 5 + 2 = 7 AnswerAnswer= 30 secAnswer

Dead Heat:- A dead Heat is a situation when all participants reaches the finish point at the same instant of time.

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