AN OBJECT MOVES WITH ACCELERATION "ALPHA" FOR SOME TIME AND "BETA"FOR ANOTHER TIME.THE OBJECT STARTS FROM REST AND IN ANOTHER HALF FINALLY COMES TO REST .THE EVENT TAKES PLACE IN TIME "t".FIND THE MAXIMUM VELOCITH ATTAIED AND TOTAL DISTANCE TRAVELLED BY THE OBJECT? 

Asked by ENGLISH DSOUZA | 4th Jun, 2014, 06:12: AM

Expert Answer:

The question is not formulated properly:- First I formulate the question
 
Question:-
 
An oobject strats from rest and moves with acceleration α for time t1. Then the particle moves with acceleration β for time t2. Then finally the particle comes to rest in time t3. Find the maximum speed and the total distance travelled.
 
Answer:-
For duration t1 :- distance travelled S1 = begin mathsize 12px style 1 half alpha t subscript 1 superscript 2 end style and final velocity v1 = α t 
For duration t2:- distance travelled S2 = begin mathsize 12px style alpha t subscript 1 t subscript 2 plus 1 half beta space t subscript 2 superscript 2 end style and final velocity v2 = begin mathsize 12px style alpha t subscript 1 space plus space beta t subscript 2 end style
for duration t3 :- retardation = begin mathsize 12px style fraction numerator alpha t subscript 1 space plus space beta space t subscript 2 over denominator t subscript 3 end fraction end style  and distance travelled  S3 = begin mathsize 12px style open parentheses alpha space t subscript 1 space plus space beta space t subscript 2 close parentheses space t subscript 3 space minus space 1 half space open parentheses fraction numerator alpha space t subscript 1 space plus space beta space t subscript 2 over denominator t subscript 3 end fraction close parentheses t subscript 3 superscript 2 space equals space 1 half open parentheses alpha space t subscript 1 space plus space beta space t subscript 2 space close parentheses space t subscript 3 end style
 
total distance travelled = S1+S2+S3; maximum speed = begin mathsize 12px style alpha t subscript 1 space plus space beta t subscript 2 end style

Answered by  | 5th Jan, 2018, 05:27: PM